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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=−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=−b2a.

3=−b2ab=−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−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+−6a8+16=064a−48a+16=016a=−16a=−1616=−1

Therefore, the value of b is

b=−6a=−6−1=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=−x2+6x+16

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

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Most popular questions from this chapter

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