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Chapter 9: Q. 240 (page 944)

In the following functions, find

a) the equation of the axis of symmetry and

b) the vertex of its graph.

f(x)=-2x2-8x-3

Short Answer

Expert verified

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

x=-2.

Part (b) The vertex is -2,5.

Step by step solution

01

Step 1. Given information.

The given expression is,

f(x)=-2x2-8x-3.

02

Step 2. Solving part (a).

On comparing the given function with the standard form then

f(x)=ax2+bx+ca=-2,b=-8,c=-3.

Substituting in the below equation we get,

x=-b2ax=--8-4x=-2

Therefore, the equation of the axis of the symmetry is x=-2.

03

Step 3. Solving part (b).

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

x=-2

Substitute the above coordinate in the given function we get

f(-2)=-2-22-8-2-3=-24+16-3=-8+16-3=5

Therefore, the vertex is -2,5.

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