Receiving Helpdesk

how do you shift a parabola left and right

by Roel Schuster III Published 3 years ago Updated 3 years ago

Explanation: The parent function for a parabolic function
parabolic function
A quadratic function is a function that can be written in the form f(x)=ax2+bx+c where a,b, and c are real numbers and a≠0. This form is called the standard form of a quadratic function. The graph of the quadratic function is a U-shaped curve is called a parabola.
https://www.varsitytutors.com › hotmath › topics › parabolas

Parabolas - Varsity Tutors

 is where is the center of the parabola. To shift the parabola left of right, the value of h changes. Since there is a negative sign in the parent function, a positive value moves the parabola to the left and a negative value moves it to the right.

How to move a parabola from left to right?

  • The x-axis is horizontal; the y-axis is vertical.
  • The positive numbers on the y-axis are above the point (0, 0), and the negative numbers on the y-axis are below the point (0, 0).
  • The positive numbers on the x-axis are to the right of the point (0, 0), and the negative numbers on the x-axis are to the left of the point (0, ...

How to transform a parabola?

  • y = x2 + 6x + 8 [original quadratic equation corresponding to the parabola]
  • y – 3 = x2 + 6x + 8 [substitute y – 3 for y]
  • y = x2 + 6x + 8 + 3 [add 3 to both sides to solve for y]
  • y = x2 + 6x + 11 [combine like terms]

What is the formula for a sideways parabola?

What is the formula for a sideways parabola? The “general” form of a parabola’s equation is the one you’re used to, y = ax2 + bx + c — unless the quadratic is “sideways”, in which case the equation will look something like x = ay2 + by + c.

How can I do an arithmetic shift left?

An arithmetic shift via micro operation that shifts a signed binary number to the left and right. A logical shift is one that transforms through the serial input. 2. An arithmetic shift left multiplies assigned binary number by. An arithmetic shift right divides number by 2. The symbols strand and for logical shift left and logical shift right ...

How To Move A Parabola To The Right Or Left (Horizontal Shift)

To move a parabola H units to the right, you would substitute x – H for x in the corresponding quadratic equation. This is called a horizontal shift.

How To Move A Parabola Up Or Down (Vertical Shift)

To move a parabola V units up, you would substitute y – H for Y in the corresponding quadratic equation. This is called a vertical shift.

How To Make A Parabola Upside Down (Negative Reflection Or Concavity Change)

Remember that a quadratic in standard form has the equation f (x) = ax 2 + bx + c. The coefficient of x 2, a, will determine the concavity of the parabola (whether it opens up or down):

Combining Multiple Shifts & Transformations

Of course, we can also combine multiple shifts and transformations with the same parabola.

Recent Posts

The Law of Cosines is useful in geometry and trigonometry when we solve triangles (to find their side lengths and angle measures). So, what is the Law of Cosines? The Law of Cosines relates...

image

Popular Posts:

  • 1. is the book hatchet fiction or nonfiction
  • 2. can you buy carprofen over the counter
  • 3. millimeters to centimeters to inches
  • 4. how do i reset my whirlpool side by side ice maker
  • 5. el sistema solar en ingles
  • 6. how much does an ssbi cost
  • 7. how wide is a plastic 55 gallon drum
  • 8. are stay green bites safe for dogs
  • 9. where is parker schnabel today
  • 10. escritura inca quipus
    • A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
    Messages11TimelineExceptionsViews7RouteQueries7Models15Livewire0MailsGateSessionRequest
    8.3.21PHP Version2.48sRequest Duration2MBMemory UsageGET {post}Route
    • warninglog[11:00:31] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
    • warninglog[11:00:31] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
    • warninglog[11:00:31] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
    • warninglog[11:00:31] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
    • warninglog[11:00:31] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[11:00:31] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    warning
    • Booting (12.66ms)
    • Application (2.47s)
    • 1 x Application (99.47%)
      2.47s
      1 x Booting (0.51%)
      12.66ms
      7 templates were rendered
      • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
        Params
        0
        post
        1
        postContent
        2
        author
        3
        updated_at
        4
        bing_rich_snippet_text
        5
        bing_rich_snippet_link
        6
        bing_related_keywords
        7
        google_related_keywords
        8
        bing_news_title
        9
        bing_news_description
        10
        bing_videos
        11
        bing_images
        12
        bing_search_result_title
        13
        bing_search_result_description
        14
        bing_search_result_url
        15
        bing_paa_questions
        16
        bing_paa_answers
        17
        bing_slider_faq_questions
        18
        bing_slider_faq_answers
        19
        bing_pop_faq_questions
        20
        bing_pop_faq_answers
        21
        bing_tab_faq_questions
        22
        bing_tab_faq_answers
        23
        google_faq_questions
        24
        google_faq_answers
        25
        google_rich_snippet
        26
        google_search_result
        27
        indexedArray
        28
        total_images
        29
        total_videos
        30
        settings
        31
        url_current
        32
        menus
        33
        sidebar
      • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      uri
      GET {post}
      middleware
      web, checkdate
      as
      post.show
      controller
      App\Http\Controllers\Frontend\json_data\PostController@show
      namespace
      where
      file
      app/Http/Controllers/Frontend/json_data/PostController.php:18-166
      7 statements were executed2.45s
      receivinghelpdeskask
      • select * from `posts` where `published_at` <= '2025-07-08 11:00:31' and `slug` = 'how-do-you-shift-a-parabola-left-and-right' and `posts`.`deleted_at` is null limit 1
        2.9ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
        Metadata
        Bindings
        • 0. 2025-07-08 11:00:31
        • 1. how-do-you-shift-a-parabola-left-and-right
        Backtrace
        • 15. /app/Providers/RouteServiceProvider.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
        • 19. Route binding:39
        • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
      • select * from `json_post_contents` where `json_post_contents`.`post_id` = 186902 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
        4.39msmiddleware::checkdate:30receivinghelpdeskask
        Metadata
        Bindings
        • 0. 186902
        • 1. 0
        Backtrace
        • 19. middleware::checkdate:30
        • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
        • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • select * from `nova_menu_menus` where `slug` = 'header' limit 1
        870μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
        Metadata
        Bindings
        • 0. header
        Backtrace
        • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
        280μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
        • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
        220μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
        Metadata
        Backtrace
        • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
        • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
        • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
        2.44s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
        Metadata
        Bindings
        • 0. publish
        Backtrace
        • 14. /app/View/Composers/SidebarView.php:22
        • 15. /app/View/Composers/SidebarView.php:12
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `fake_users` where `fake_users`.`id` = 42004 limit 1
        710μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
        Metadata
        Bindings
        • 0. 42004
        Backtrace
        • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
        • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      App\Models\FakeUser
      1
      Outl1ne\MenuBuilder\Models\MenuItem
      1
      Outl1ne\MenuBuilder\Models\Menu
      1
      App\Models\JsonPostContent
      1
      App\Models\Post
      11
          _token
          bnDiPp6cTHZpUBsjAZOmTv2iBoaYGwgcEgZR886Q
          _previous
          array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-do-you-shift-a-parabola-left-and-right" ...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /how-do-you-shift-a-parabola-left-and-right
          status_code
          200
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          request_request
          []
          request_headers
            0 of 0   
          array:24 [▼
  "cf-ipcountry" => array:1 [▶
    0 => "US"
  ]
  "cf-connecting-ip" => array:1 [▶
    0 => "216.73.216.119"
  ]
  "cdn-loop" => array:1 [▶
    0 => "cloudflare; loops=1"
  ]
  "sec-fetch-site" => array:1 [▶
    0 => "none"
  ]
  "accept" => array:1 [▶
    0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  ]
  "user-agent" => array:1 [▶
    0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  ]
  "upgrade-insecure-requests" => array:1 [▶
    0 => "1"
  ]
  "sec-ch-ua-platform" => array:1 [▶
    0 => ""Windows""
  ]
  "sec-ch-ua-mobile" => array:1 [▶
    0 => "?0"
  ]
  "sec-ch-ua" => array:1 [▶
    0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99""
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "sec-fetch-dest" => array:1 [▶
    0 => "document"
  ]
  "cf-ray" => array:1 [▶
    0 => "95bd30abeb4dabb8-YYZ"
  ]
  "accept-encoding" => array:1 [▶
    0 => "gzip, br"
  ]
  "priority" => array:1 [▶
    0 => "u=0, i"
  ]
  "sec-fetch-user" => array:1 [▶
    0 => "?1"
  ]
  "sec-fetch-mode" => array:1 [▶
    0 => "navigate"
  ]
  "cf-visitor" => array:1 [▶
    0 => "{"scheme":"https"}"
  ]
  "connection" => array:1 [▶
    0 => "close"
  ]
  "x-forwarded-proto" => array:1 [▶
    0 => "https"
  ]
  "x-forwarded-for" => array:1 [▶
    0 => "216.73.216.119, 172.69.130.70"
  ]
  "x-server-addr" => array:1 [▶
    0 => "154.12.239.204"
  ]
  "host" => array:1 [▶
    0 => "receivinghelpdesk.com"
  ]
]
          request_server
            0 of 0   
          array:55 [▼
  "USER" => "runcloud"
  "HOME" => "/home/runcloud"
  "SCRIPT_NAME" => "/ask/index.php"
  "REQUEST_URI" => "/ask/how-do-you-shift-a-parabola-left-and-right"
  "QUERY_STRING" => ""
  "REQUEST_METHOD" => "GET"
  "SERVER_PROTOCOL" => "HTTP/1.0"
  "GATEWAY_INTERFACE" => "CGI/1.1"
  "REDIRECT_URL" => "/ask/how-do-you-shift-a-parabola-left-and-right"
  "REMOTE_PORT" => "44460"
  "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php"
  "SERVER_ADMIN" => "you@example.com"
  "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/"
  "CONTEXT_PREFIX" => ""
  "REQUEST_SCHEME" => "http"
  "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/"
  "REMOTE_ADDR" => "172.69.130.70"
  "SERVER_PORT" => "80"
  "SERVER_ADDR" => "127.0.0.1"
  "SERVER_NAME" => "receivinghelpdesk.com"
  "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f"
  "SERVER_SIGNATURE" => ""
  "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib"
  "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
  "HTTP_CF_IPCOUNTRY" => "US"
  "HTTP_CF_CONNECTING_IP" => "216.73.216.119"
  "HTTP_CDN_LOOP" => "cloudflare; loops=1"
  "HTTP_SEC_FETCH_SITE" => "none"
  "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  "HTTP_UPGRADE_INSECURE_REQUESTS" => "1"
  "HTTP_SEC_CH_UA_PLATFORM" => ""Windows""
  "HTTP_SEC_CH_UA_MOBILE" => "?0"
  "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99""
  "HTTP_CACHE_CONTROL" => "no-cache"
  "HTTP_PRAGMA" => "no-cache"
  "HTTP_SEC_FETCH_DEST" => "document"
  "HTTP_CF_RAY" => "95bd30abeb4dabb8-YYZ"
  "HTTP_ACCEPT_ENCODING" => "gzip, br"
  "HTTP_PRIORITY" => "u=0, i"
  "HTTP_SEC_FETCH_USER" => "?1"
  "HTTP_SEC_FETCH_MODE" => "navigate"
  "HTTP_CF_VISITOR" => "{"scheme":"https"}"
  "HTTP_CONNECTION" => "close"
  "HTTP_X_FORWARDED_PROTO" => "https"
  "HTTP_X_FORWARDED_FOR" => "216.73.216.119, 172.69.130.70"
  "HTTP_X_SERVER_ADDR" => "154.12.239.204"
  "HTTP_HOST" => "receivinghelpdesk.com"
  "HTTPS" => "on"
  "REDIRECT_STATUS" => "200"
  "REDIRECT_HTTPS" => "on"
  "FCGI_ROLE" => "RESPONDER"
  "PHP_SELF" => "/ask/index.php"
  "REQUEST_TIME_FLOAT" => 1751952631.7552
  "REQUEST_TIME" => 1751952631
]
          request_cookies
          []
          response_headers
            0 of 0   
          array:7 [▼
  "content-type" => array:1 [▶
    0 => "text/html; charset=UTF-8"
  ]
  "cache-control" => array:1 [▶
    0 => "private, must-revalidate"
  ]
  "date" => array:1 [▶
    0 => "Tue, 08 Jul 2025 05:30:31 GMT"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "expires" => array:1 [▶
    0 => -1
  ]
  "set-cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IktGM2hnYlhIM3RIVmliTFBQamNlZVE9PSIsInZhbHVlIjoiRzhpeXhIQkJBOVhEbGxVTW9jZHI2bGUwT2VOdS9RZWxlWFVObldjRVZ3bGFWRG5hZlBqaHF3NFF4b3JXNDh2eXhjWWttWUJyc3Vvd2MxOWx3N29vU25KNCtvNnF0OXA5RUxmeTIrei9ZSTduL2xvRW12aXlwZTV0T0ZveXg4aXMiLCJtYWMiOiJkYTdkYjExNGViNmZhZGRkMGYyOGU1MjI1NjlmODM1OGQ1NDlmOTZkYWQxZTI2Y2E3MTZhMzNlNmJjZjJhNjI5IiwidGFnIjoiIn0%3D; expires=Tue, 08-Jul-2025 07:30:34 GMT; Max-Age=7200; path=/; samesite=lax ◀XSRF-TOKEN=eyJpdiI6IktGM2hnYlhIM3RIVmliTFBQamNlZVE9PSIsInZhbHVlIjoiRzhpeXhIQkJBOVhEbGxVTW9jZHI2bGUwT2VOdS9RZWxlWFVObldjRVZ3bGFWRG5hZlBqaHF3NFF4b3JXNDh2eXhjWWttW ▶"
    1 => "askhelpdesk_session=eyJpdiI6IkpHem1BZkljSExBL3oyTFMwR1oxdVE9PSIsInZhbHVlIjoiOGVEVy9wbmdnT2pQd2JPTVplNzBlNTVXTkhhSHIyQUVzWFkvWUZRdG9DNTZnWG1ZN1NOelQ5d0dybnd6L2Npc0Q0cllyRlA0UFBMMHFQZ0tiTTJ5Q3FPNlRvU1U5QmRiS0g4Vlg4SmxDbmxBVDZEZ3FoWVVCQklwMWVENUhWSEwiLCJtYWMiOiI1MmMyYjE0NjlkZjcxOTlkNDM4ZDk5NmM3OGRhZjU3YjRhNTFiZDczMzAxOTAxMzY5MjkzMmU4Y2Y0ZDIxMjEyIiwidGFnIjoiIn0%3D; expires=Tue, 08-Jul-2025 07:30:34 GMT; Max-Age=7200; path=/; httponly; samesite=lax ◀askhelpdesk_session=eyJpdiI6IkpHem1BZkljSExBL3oyTFMwR1oxdVE9PSIsInZhbHVlIjoiOGVEVy9wbmdnT2pQd2JPTVplNzBlNTVXTkhhSHIyQUVzWFkvWUZRdG9DNTZnWG1ZN1NOelQ5d0dybnd6L2Np ▶"
  ]
  "Set-Cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IktGM2hnYlhIM3RIVmliTFBQamNlZVE9PSIsInZhbHVlIjoiRzhpeXhIQkJBOVhEbGxVTW9jZHI2bGUwT2VOdS9RZWxlWFVObldjRVZ3bGFWRG5hZlBqaHF3NFF4b3JXNDh2eXhjWWttWUJyc3Vvd2MxOWx3N29vU25KNCtvNnF0OXA5RUxmeTIrei9ZSTduL2xvRW12aXlwZTV0T0ZveXg4aXMiLCJtYWMiOiJkYTdkYjExNGViNmZhZGRkMGYyOGU1MjI1NjlmODM1OGQ1NDlmOTZkYWQxZTI2Y2E3MTZhMzNlNmJjZjJhNjI5IiwidGFnIjoiIn0%3D; expires=Tue, 08-Jul-2025 07:30:34 GMT; path=/ ◀XSRF-TOKEN=eyJpdiI6IktGM2hnYlhIM3RIVmliTFBQamNlZVE9PSIsInZhbHVlIjoiRzhpeXhIQkJBOVhEbGxVTW9jZHI2bGUwT2VOdS9RZWxlWFVObldjRVZ3bGFWRG5hZlBqaHF3NFF4b3JXNDh2eXhjWWttW ▶"
    1 => "askhelpdesk_session=eyJpdiI6IkpHem1BZkljSExBL3oyTFMwR1oxdVE9PSIsInZhbHVlIjoiOGVEVy9wbmdnT2pQd2JPTVplNzBlNTVXTkhhSHIyQUVzWFkvWUZRdG9DNTZnWG1ZN1NOelQ5d0dybnd6L2Npc0Q0cllyRlA0UFBMMHFQZ0tiTTJ5Q3FPNlRvU1U5QmRiS0g4Vlg4SmxDbmxBVDZEZ3FoWVVCQklwMWVENUhWSEwiLCJtYWMiOiI1MmMyYjE0NjlkZjcxOTlkNDM4ZDk5NmM3OGRhZjU3YjRhNTFiZDczMzAxOTAxMzY5MjkzMmU4Y2Y0ZDIxMjEyIiwidGFnIjoiIn0%3D; expires=Tue, 08-Jul-2025 07:30:34 GMT; path=/; httponly ◀askhelpdesk_session=eyJpdiI6IkpHem1BZkljSExBL3oyTFMwR1oxdVE9PSIsInZhbHVlIjoiOGVEVy9wbmdnT2pQd2JPTVplNzBlNTVXTkhhSHIyQUVzWFkvWUZRdG9DNTZnWG1ZN1NOelQ5d0dybnd6L2Np ▶"
  ]
]
          session_attributes
            0 of 0   
          array:4 [▼
  "_token" => "bnDiPp6cTHZpUBsjAZOmTv2iBoaYGwgcEgZR886Q"
  "_previous" => array:1 [▶
    "url" => "https://receivinghelpdesk.com/ask/how-do-you-shift-a-parabola-left-and-right"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]