Question

Write a quadratic function whose zeros are -12 and -2.

Answer 1

(x+12) (x+2)

x(x+12)+2(x+12)

x^2+12x+2x+24

x^2+14x+24

Explanation:

Answer 2

f(x) = x² + 14x + 24

Explanation:

Given the zeros of -12 and -2, then it means that:

x + 12 = 0 and x + 2 = 0

As a proof, if you isolate x, you'll end up with the given values:

x + 12 - 12 = 0 - 12

x = -12

x + 2 - 2 = 0 - 2

x = -2

In terms of using these values into the quadratic function:

(x + 12) (x + 2)

Perform the FOIL method in order to find the quadratic function:

(x + 12) (x + 2)

f(x) = x² + 2x + 12x + 24

f(x) = x² + 14x + 24 ⇒ This is the quadratic function, given the zeros as x = -12, and x = -2.