7.11.5 Graphs of Quadratic Functions

Algebra 17.11.5 Graphs of Quadratic Functions

Search for key terms or text.

Cool Down

The function $f$ is given by $f (x) = (x - 2) (x + 4)$ .

Without using graphing technology, answer questions 1 – 4.

What are the $x$ -intercepts of the graph representing $f$ ?

Compare your answer:

$x$ -intercepts for function $f$ : $(2, 0)$ and $(- 4, 0)$

What is the $x$ -coordinate of the vertex of the graph?

-1

What is the $y$ -coordinate of the vertex of the graph?

-9

What is the $y$ -intercept?

Compare your answer:

The $y$ -intercept is $(0, - 8)$ , because $(0 - 2) (0 + 4) = (- 2) (4) = - 8$ .

Access multimedia content

Use the graphing tool or technology outside the course. Sketch a graph that represents $f$ .

Compare your answer:

The graph opens upward with vertex at $(- 1, - 9)$ and $x$ -intercepts at $(2, 0)$ and $(- 4, 0)$ .

A parabola on a coordinate grid. The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 2 and extends from negative 12 to 12.

Previous Next

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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/7-11-5-graphs-of-quadratic-functions

© 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.