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Chapter 9: Q. 239 (page 944)

In the following functions, find

a) the equation of the axis of symmetry and

b) the vertex of its graph.

f(x)=-x2+2x+5

Short Answer

Expert verified

Part (a) The equation of the axis of symmetry is

x=1.

Part (b) The vertex is1,6.

Step by step solution

01

Step 1. Given information.

The given expression is,

f(x)=-x2+2x+5.

02

Step 2. Solving part (a).

On comparing the given function with the standard form then,

f(x)=ax2+bx+ca=-1,b=2,c=5.

Substituting in the below equation we get,

x=-b2ax=-2-2x=1

Therefore, the equation of the axis of symmetry isx=1.

03

Step 3. Solving part (b).

Here, the vertex is a point on the symmetric line we have

x=1

Substitute the above coordinate in the given function we get

f(1)=-12+21+5=-1+2+5=6

Therefore, the vertex is 1,6.

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