Question

The zeros of a quadratic function are –7 and 3. Which of the following could be the function? Select all that apply:

f(x)=x^2+4x-21
f(x)=x^2-4x-21
f(x)=2x^2-8x-42
f(x)=5x^2+20x-105

Answer 1

Explanation:

f(x) = (x+7)(x-3)

= x²+4x-21 ... (option A)

Answer 2

First option: f(x)=x^2+4x-21

AND

Fourth option: f(x)=5x^2+20x-105

Explanation:

All you have to do is do the quadratic equation backwards

If the zeros are x=-7 and x=3, the equation would look like ->

(x+7)(x-3)

Now distribute it

x(x-3)+7(x-3)

x^2-3x+7x-21

x^2+4x-21

The Fourth option is also correct. Just divide the whole equation by 5 and you will get the same exact equation as the first option.