Question

Identify the range of the equation y = −x2 − 12x + 3.

All real numbers

y ≤ 39

y ≥ −6

y ≤ −105

Answer 1

\[\large y=-x^2-12x+3\]


\[\large y=-(x^2+12x-3)\]


\[\large y=-(x^2+12x+36-36-3)\]


\[\large y=-((x^2+12x+36)-36-3)\]


\[\large y=-((x+6)^2-36-3)\]


\[\large y=-((x+6)^2-39)\]


\[\large y=-(x+6)^2+39\]


Graph is a parabola that opens downward, so the max value of y is 39


So the range is \[y \le 39\] so the answer is choice B