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Chapter 10: Q 303. (page 1238)

In the following exercises, find 鈸� the axis of symmetry and 鈸� the vertex.

y=-x2+6x+8

Short Answer

Expert verified

Part (a)x=3

Part (b)3,17

Step by step solution

01

Part (a) Step 1. Given information.

The given information is:

y=-x2+6x+8

02

Part (a) Step 2. Find the axis of symmetry.

y=ax2+bx+cy=-x2+6x+8

The axis of symmetry is the line role="math" localid="1653822327107" x=-b2a.

Substitute the values of a, and binto the equation.

x=-62-1x=3

Therefore, the axis of symmetry isx=3.

03

Part (b) Step 1. Find the vertex.

The vertex is on the line of symmetry, so its x-coordinate will be x=3.

Now substitute the value of xinto the equation,

y=-x2+6x+8=-32+63+8=-9+18+8=17

Therefore the vertex is (3,17).

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