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Chapter 9: Q70. (page 534)

CHALLENGE Using the axis of symmetry and one x-intercept, write an equation for the graph shown.

Short Answer

Expert verified

The equation for given graph is y=鈭�x2+6x+16.

Step by step solution

01

Step 1. Axis of symmetry.

From the graph, it can be observed that the vertex of a parabola is 3,25. Therefore, the axis of symmetry is x=3.

02

Step 2. Substitution.

Substitute the value of x in the equation, x=鈭�b2a.

3=鈭�b2ab=鈭�6a

03

Step 3. Y-intercept and x-intercept.

From the graph, it can be observed that the y-intercept is c=16. The parabola has x-intercept at鈭�2,0 and 8,0.

04

Step 4. Substitution.

Substitute8,0 for x,y, 16 for c and-6 for b into y=ax2+bx+c.

a82+鈭�6a8+16=064a鈭�48a+16=016a=鈭�16a=鈭�1616=鈭�1

Therefore, the value of b is

b=鈭�6a=鈭�6鈭�1=6

05

Step 5. Write equation for given graph.

Substitute -1 for a, 6 for b and 16 for c in the standard form of quadratic equation.

y=ax2+bx+c=鈭�x2+6x+16

Therefore, the equation for given graph is y=鈭�x2+6x+16.

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Most popular questions from this chapter

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

x2鈭�10x=鈭�15

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

x2+8=鈭�6x

Which is an equation for the function shown in the graph?

Ay=鈭�3x2

By=3x2+1

Cy=x2+2

Dy=鈭�3x2+2

Considery=x2鈭�5x+4

Write the equation of the axis of symmetry.

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of a quadratic function is a straight line.
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