write a quadratic function with zeros 7 and -4. write your answer using the variable x and in standard form…

write a quadratic function with zeros 7 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 7 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 zeros of a quadratic function, then the function can be written in factored form as (f(x)=k(x - a)(x - b)). Here (a = 7), (b=-4) and (k = 1), so (f(x)=(x - 7)(x+4)).

Step2: Expand the factored form

Using the FOIL method ((x - 7)(x + 4)=x\times x+x\times4-7\times x - 7\times4). [ \begin{align*} &x^{2}+4x-7x - 28\ =&x^{2}-3x - 28 \end{align*} ]

Answer:

(x^{2}-3x - 28)