Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

7.12.4 Representations of Quadratic Functions

Algebra 17.12.4 Representations of Quadratic Functions

Search for key terms or text.

Activity

Your teacher will give your group a set of cards. Each card contains a graph or an equation.

  • Take turns with your partner to sort the cards into sets so that each set contains two equations and a graph that all represent the same quadratic function.

  • For each set of cards that you put together, explain to your partner how you know they belong together.

  • For each set that your partner puts together, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

Once all the cards are sorted and discussed, record the equivalent equations, sketch the corresponding graph, and write a brief note or explanation about why the representations were grouped together.

Self Check

Examine the graph below.

GRAPH OF A PARABOLA THAT OPENS UPWARD WITH A \(y\)-intercepts OF NEGATIVE 2 AND \(x\)-intercepts OF NEGATIVE 2 AND 1.

Which function matches the graph?

  1. f ( x ) = ( x 2 ) ( x 1 )
  2. f ( x ) = ( x + 2 ) ( x + 1 )
  3. f ( x ) = ( x + 2 ) ( x 1 )
  4. f ( x ) = ( x 2 ) ( x + 1 )

Additional Resources

Matching Quadratic Functions and Their Graphs

Below is a quadratic function represented in standard form, factored form, and with a graph.

Standard Form: f ( x ) = x 2 + 2 x 8 f ( x ) = x 2 + 2 x 8

Factored Form: f ( x ) = ( x + 4 ) ( x 2 ) f ( x ) = ( x + 4 ) ( x 2 )

A parabola on a coordinate grid. The x-axis scale is 1 and extends from negative 10 to 10. The y-axis scale is 1 and extends from negative 14 to 6.

Notice the factored form helps find the zeros: x = 4 x = 4 and x = 2 x = 2 .

The factored form gives the zeros since the zeros ( x x -intercepts) are located where each factor equals 0.

The standard form, f ( x ) = x 2 + 2 x 8 f ( x ) = x 2 + 2 x 8 , helps give the y y -intercept. The y y -intercept occurs when x = 0 x = 0 . Here, f ( 0 ) = 8 f ( 0 ) = 8 . On the graph, the y y -intercept is ( 0 , 8 ) ( 0 , 8 ) .

Try it

Try It: Matching Quadratic Functions and Their Graphs

Given the graph below and its function in standard form and factored form, identify all intercepts.

A parabola on a coordinate grid. The x-axis scale is 1 and extends from negative 10 to 10. The y-axis scale is 1 and extends from negative 14 to 6.

Standard form: f ( x ) = x 2 x 6 f ( x ) = x 2 x 6 Factored form: f ( x ) = ( x 3 ) ( x + 2 ) f ( x ) = ( x 3 ) ( x + 2 )

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.