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Q17.

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Algebra 2
Found in: Page 291
Algebra 2

Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

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Short Answer

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-9

  1. The y-intercept is -9, equation of axis of symmetry is x=0and x-coordinate of vertex is 0.
  2. The table is:

Here, the vertex is 0,-9

c. The graph is:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

aStep 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a≠0

  • The y-intercept is f(x)=a02+b0+c or c
  • The equation of axis of symmetry is x=-b2a
  • The x-coordinate of vertex is -b2a

Step 2. Given Information.

The given function is f(x)=x2-9

Step 3. Solution.

In the function f(x)=x2-9, we have a=1,b=0,c=-9

So, the y-intercept is -9.

The equation of axis of symmetry is given by x=-b2a

Substitute the values a=1,b=0 to get:

x=−02(1)...............a=1,b=0⇒x=0

So, the equation of axis of symmetry is x=0. Therefore, the x-coordinate of vertex is 0.

bStep 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a≠0

  • The y-intercept is f(x)=a02+b0+c or c
  • The equation of axis of symmetry is x=-b2a
  • The x-coordinate of vertex is -b2a

Step 2. Given Information.

The given function is f(x)=x2-9.

From part (a), we have y-intercept is -9, equation of axis of symmetry is x=0 and x-coordinate of vertex is 0.

Step 3. Discussion.

Choose some values for x that are less than 0 and some that are greater than 0. This ensures that points on each side of the axis of symmetry are graphed.

Step 4. Table.

Here, the vertex is ( 0,-9)

cStep 1. Use the concept.

The graph of f(x)=ax2+bx+c,a≠0

  • The y-intercept is f(x)=a02+b0+c or c
  • The equation of axis of symmetry is x=-b2a
  • The x-coordinate of vertex is -b2a

Step 2. Given Information.

The given function is f(x)=x2-9

From part (a) and (b), we have

Here, the vertex is 0,-9, the y-intercept is -9, equation of axis of symmetry is x=0.

Step 3. Solution.

Graph the vertex and y-intercept. Then graph the points from your table connecting them and the y-intercept with a smooth curve. As a check, draw the axis of symmetry, x=0, as a green line. The graph of the function should be symmetrical about this line.

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  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

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