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Chapter 6: Q56. (page 292)

The graph of which of the following equations is symmetrical about the y-axis?

  1. y=x2+3x-1
  2. y=-x2+x
  3. y=6x2+9
  4. y=3x2-3x+1

Short Answer

Expert verified

C. Among the given equations, the graph which is symmetrical about the y-axis is y=6x2+9.

Step by step solution

01

Step 1. Given Information.

Given to determine which among the given equations is symmetrical about the y-axis.

02

Step 2. Explanation.

The equation of y-axis is x=0

For an equation of the form fx=ax2+bx+c, the axis of symmetry is given by x=-b2a

For y=x2+3x-1:

The axis of symmetry is:

x=鈭�b2ax=鈭�321x=鈭�32

Hence the graph is not symmetrical about y axis.

For y=-x2+x:

The axis of symmetry is:

x=鈭�b2ax=鈭�12鈭�1x=12

Hence the graph is not symmetrical about y axis.

For y=6x2+9:

The axis of symmetry is:

x=鈭�b2ax=鈭�026x=0

Hence the graph is symmetrical about y axis.

For y=3x2-3x+1:

The axis of symmetry is:

x=鈭�b2ax=鈭�鈭�323x=12

Hence the graph is not symmetrical about y axis.

03

Step 3. Conclusion.

Among the given equations, the graph which is symmetrical about the y-axis is

y=6x2+9.

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Most popular questions from this chapter

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=4x-x2+1

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=7x2+4x+1

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)=-3x2-4x

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+8x+3

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=0.5x2-1
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