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Chapter 9: Q. 238 (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+10x+25

Short Answer

Expert verified

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

x=-5.

Part (b) The vertex is-5,0.

Step by step solution

01

Step 1. Given information.

The given expression is

f(x)=x2+10x+25.

02

Step 2. Solving part (a).

On comparing the given function with the standard form then

f(x)=ax2+bx+ca=1,b=10,c=25.

Substituting in the below equation we get,

x=-b2ax=-102x=-5

Therefore, the equation of the axis of symmetry isx=-5.

03

Step 3. Solving part (b).

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

x=-5

Substitute the above coordinate in the given function we get

f(-5)=-52+10-5+25=25-50+25=50-50=0

Therefore, the vertex is-5,0.

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