Question

Select ALL choices that are zeros of this function y=x2 +12x +32
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Answer 1

{-8, -4}

Explanation:

Rewrite this function y=x2 +12x +32 as y = x^2 + 12x + 32; " ^ " indicates exponentiation.

Set this x^2 + 12x + 32 equal to zero (to find the zeros):

x^2 + 12x + 32 = 0. Let's solve this using the quadratic formula, which applies when ax^2 + bx + c = 0:

-b ± √(b^2 - 4·a·c)

x = -------------------------------

2a

The coefficients of the given quadratic are {1, 12, 32}. Thus, the discriminant is

b^2 - 4ac, or 12^2 - 4(1)(32), or 144 - 128, or 16. Therefore, we have:

-12 ± √16 -12 ± 4

x = -------------------- which simplifies to: x = --------------- = { -8, -4}

2 2

The zeros are {-8, -4}