Answer:
[tex]f(x)=-0.5x^2+x+4[/tex]
Step-by-step explanation:
we know that
A quadratic function in factored form is equal to
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
where
a is the leading coefficient
x_1 and x_2 are the zeroes of the function
substitute the given values
[tex]f(x)=a(x-4)(x+2)[/tex]
Find the value of a
Remember that
For x=0 ----> f(0)=4
substitute
[tex]4=a(0-4)(0+2)[/tex]
[tex]4=a(-8)\\a=-0.5[/tex]
so
[tex]f(x)=-0.5(x-4)(x+2)[/tex]
[tex]f(x)=-0.5(x^2+2x-4x-8)[/tex]
[tex]f(x)=-0.5(x^2-2x-8)[/tex]
[tex]f(x)=-0.5x^2+x+4[/tex]