Question

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

Answer 1

Answer:

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

Step-by-step 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

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

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

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

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