Question

Please help, I don't know how to do this.

f(x)=(x+2)(x−4)
1) What are the zeros of the function?
2) What is the vertex of the parabola?

Answer 1

(a) Zeroes of the function is -2,4.

(b) The vertex of the parabola is (1,-9).

Explanation:

Given,

f(x)=(x+2)(x−4)

(a)To find the zeros of the function put f(x)=0.

(x+2)(x-4)=0

x+2 = 0 or x-4 = 0

x = -2,4

Hence, zeroes of the function is -2,4.

(b)Now,

f(x)=(x+2)(x−4)

`f(x)= x^2 -2x+1 -1-8`

`f(x)= (x-1)^2-9` .......(i)

We know that,

If
`f(x)=a(x-h)^2 +k` is the equation of parabola the (h,k) is the vertex of the parabola.

On comparing with equation (i), we get

h = 1

k = -9

Hence, the vertex of the parabola is (1,-9).