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Chapter 10: Q 304. (page 1238)

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

y=2x2-8x+1

Short Answer

Expert verified

Part (a)x=2

Part (b)2,-7

Step by step solution

01

Step 1. Given information.

The given information is:

y=2x2-8x+1

02

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

y=ax2+bx+cy=2x2-8x+1

The axis of symmetry is the linex=-b2a.

Substitute the values of a, and binto the equation.

x=--822x=2

Therefore, the axis of symmetry is x=2.

03

Part (b) Step 1. Find the vertex.

The vertex is on the line of symmetry, so its x-coordinate will be x=2.

Now substitute the value of xinto the equation,

role="math" localid="1653823467755" y=2x2-8x+1=222-82+1=8-16+1=-7

Therefore the vertex is 2,-7.

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