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

9.10.7 Practice

Algebra 19.10.7 Practice
Search for key terms or text.

Complete the following questions to practice the skills you have learned in this lesson.

  1. The following quadratic expressions all define the same function.
  • ( x + 5 ) ( x + 3 )
  • x 2 + 8 x + 15
  • ( x + 4 ) 2 − 1

Select three statements that are true about the graph of this function.

  1. The y -intercept is ( 0 , − 15 ) .
  2. The vertex is ( − 4 , − 1 ) .
  3. The x -intercepts are ( − 5 , 0 ) and ( − 3 , 0 ) .
  4. The x -intercepts are ( 0 , 5 ) and ( 0 , 3 ) .
  5. The x -intercept is ( 0 , 15 ) .
  6. The y -intercept is ( 0 , 15 ) .
  7. The vertex is ( 4 , − 1 ) .
  1. The following expressions all define the same quadratic function.
  • ( x − 4 ) ( x + 6 )
  • x 2 + 2 x − 24
  • ( x + 1 ) 2 − 25
  1. What is the value of the y -coordinate of the y -intercept ( 0 , _ _ _ ) of the graph of the function?
  1. Select two x -intercepts of the graph.
  1. ( 6 , 0 )
  2. ( − 4 , 0 )
  3. ( − 6 , 0 )
  4. ( 5 , 0 )
  5. ( 4 , 0 )
  1. What is the x -coordinate of the vertex of the graph?
  1. What is the y -coordinate of the vertex of the graph?
  1. Is this an accurate graph of the function?

  1. No
  2. Yes
  1. Here is one way an expression in standard form is rewritten into vertex form.

Original expression
x 2 − 7 x + 6 ;

Step 1 - x 2 − 7 x + ( − 7 2 ) 2 + 6 − ( − 7 2 ) 2

Step 2 - ( x − 7 2 ) 2 + 6 − 49 4

Step 3 - ( x − 7 2 ) 2 + 24 4 − 49 4

Step 4 - ( x − 7 2 ) 2 − 25 4

  1. In Step 1, where did the number − 7 2 come from?
  1. Only the non-linear term was divided by 2.
  2. It is half of -7 being squared.
  3. Every term in the expression was divided by 2.
  4. It is the substitute value for x .
  1. In Step 1, why was ( − 7 2 ) 2 added and then subtracted?
  1. It is subtracted to complete the square. It is added to change the value of the expression.
  2. It is added to complete the square. It is subtracted to change the value of the expression.
  3. It is subtracted to complete the square. It is added to keep the value of the expression unchanged.
  4. It is added to complete the square. It is subtracted to keep the value of the expression unchanged.
  1. What happened in Step 2?
  1. The expression is added to keep the value of the expression unchanged.
  2. The expression, which is not a perfect square, is written as a squared expression.
  3. The expression, which is a perfect square, is written as a squared expression.
  4. The expression is subtracted to keep the value of the expression unchanged.
  1. What happened in Step 3?
  1. The constant term is written as a fraction so that it has a common denominator, which makes it easier to subtract.
  2. The linear term is written as a fraction so that it has a common denominator, which makes it easier to subtract.
  3. A random term was added to complete the square.
  4. The quadratic term is written as a fraction so that it has a common denominator, which makes it easier to subtract.
  1. What does the last expression tell us about the vertex of the graph of a function defined by this expression?
  1. The vertex of the graph is at ( 5 2 , − 6 ) .
  2. The vertex of the graph is at ( 7 2 , − 6 1 4 ) .
  3. The vertex of the graph is at ( 5 2 , − 5 2 ) .
  4. The vertex of the graph is at ( − 6 1 4 , 7 2 ) .
  1. Enter the missing number, including the sign, for the expression when d ( x ) = x 2 + 12 x + 36 is written in vertex form.

d ( x ) = ( x _ _ _ ) 2 .

  1. Enter the missing numbers, including the signs, for the expression when f ( x ) = x 2 + 10 x + 21 is written in vertex form. f ( x ) = ( x + a . _ ) 2 b . _
  1. What is the value of the missing number, including the sign, in the place of the letter a?
  1. What is the value of the missing number, including the sign, for the letter b?
  1. Enter the missing numbers, including the signs, for the expression when g ( x ) = 2 x 2 − 20 x + 32 is written in vertex form. g ( x ) = a . _ ( x + b . _ ) 2 c . _
  1. What is the value of the missing number, including the sign, in place of letter a?
  1. What is the value of the missing number, including the sign, in place of letter b?
  1. What is the value of the missing number, including the sign, in place of letter c?
  1. Enter the missing numbers, including the signs, for the expression when h ( x ) = ( 4 x − 3 ) 2 is expanded to standard form. h ( x ) = ( a . _ x ) 2 + 2 ( b . _ x ) ( − 3 ) + ( c . _ ) 2
  1. What is the value of the missing number, including the sign, in place of letter a?
  1. What is the value of the missing number, including the sign, in place of letter b?
  1. What is the value of the missing number, including the sign, in place of letter c?
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.