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

9.10.3 Converting from Standard Form to Vertex Form

Algebra 19.10.3 Converting from Standard Form to Vertex Form
Search for key terms or text.

Activity

You've expanded from factored form to standard form. To learn how to convert from standard form to vertex form (of a quadratic expression), start by going backward and convert a quadratic from vertex form to standard form.

1. Rewrite (x+5)2+1(x+5)2+1 in standard form.

2. Rewrite (x−3)2−7(x−3)2−7 in standard form.

3. Think about the steps you took, and about reversing them. Try converting one or both of the expressions in standard form back into vertex form. Explain how you go about converting the expressions.

4. Test your strategy by rewriting x2+10x+9x2+10x+9 in vertex form.

5. Let's check the expression you rewrote in vertex form. Use the Desmos graphing tool or technology outside the course to graph both x2+10x+9x2+10x+9 and your new expression.

Access multimedia content

a. Does it appear that both expressions define the same function?

b. If you convert your expression in vertex form back into standard form, do you get x2+10x+9x2+10x+9?

Self Check

Which of the following is the equivalent vertex form of the expression x 2 + 14 x − 3 ?
  1. ( x + 7 ) 2 + 46
  2. ( x + 7 ) 2 − 52
  3. ( x + 7 ) 2 − 3
  4. ( x + 7 ) 2

Additional Resources

Standard to Vertex Form

Different forms are useful for finding different characteristics of quadratic functions.

Practice writing x2+8x−7x2+8x−7 into vertex form (of a quadratic expression).

Step 1 - Work to complete the square:

b=8b=8, so (b2)2=(82)2=16(b2)2=(82)2=16.

Step 2 - Add the value to create the perfect square, and subtract the value from the original constant (this is like adding 0).

x2+8x+16−7−16x2+8x+16−7−16

Step 3 - Factor the trinomial and simplify.

(x+4)2−23(x+4)2−23

Try it

Try It: Standard to Vertex Form

Convert the quadratic expression x2+16x−10x2+16x−10 to vertex form.

PreviousNext
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.