write a quadratic function with zeros -8 and -4. write your answer using the variable x and in standard form…

write a quadratic function with zeros -8 and -4. write your answer using the variable x and in standard form with a leading coefficient of 1. f(x) =

write a quadratic function with zeros -8 and -4. write your answer using the variable x and in standard form with a leading coefficient of 1. f(x) =

Answer

Explanation:

Step1: Use zero - factor form

If (x = a) and (x = b) are the zeros of a quadratic function, then the function can be written in factored form as (f(x)=(x - a)(x - b)). Here (a=-8) and (b = - 4), so (f(x)=(x+8)(x + 4)).

Step2: Expand the factored form

Using the FOIL method ((a + b)(c + d)=ac+ad+bc+bd), we have (f(x)=x\times x+x\times4+8\times x + 8\times4=x^{2}+4x+8x + 32).

Step3: Combine like - terms

Combine the (x) terms: (f(x)=x^{2}+(4x + 8x)+32=x^{2}+12x + 32).

Answer:

(x^{2}+12x + 32)