Question

Form quadratic functions given the following information:
Zeroes at 4 and –2, f(0)=4

Answer 1

`f(x)=-0.5x^2+x+4`

Explanation:

we know that

A quadratic function in factored form is equal to

`f(x)=a(x-x_1)(x-x_2)`

where

a is the leading coefficient

x_1 and x_2 are the zeroes of the function

substitute the given values

`f(x)=a(x-4)(x+2)`

Find the value of a

Remember that

For x=0 ----> f(0)=4

substitute

`4=a(0-4)(0+2)`

`4=a(-8)\\a=-0.5`

so

`f(x)=-0.5(x-4)(x+2)`

`f(x)=-0.5(x^2+2x-4x-8)`

`f(x)=-0.5(x^2-2x-8)`

`f(x)=-0.5x^2+x+4`