Provide an appropriate response.
-Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$-intercepts 3 and $- 4$ and $y$-intercept $- 24$
A) $f ( x ) = x ^ { 2 } + x - 12$
B) $f ( x ) = x ^ { 2 } + 5 x - 24$
C) $f ( x ) = x ^ { 2 } + x - 24$
D) $f ( x ) = 2 x ^ { 2 } + 2 x - 24$

Question

Quizplus · Accepted Answer

The quadratic function with x-intercepts 3 and -4 can be written as $f(x) = a(x - 3)(x + 4)$. The y-intercept is -24, so $f(0) = a(0 - 3)(0 + 4) = -24$. Solving gives $a = 2$, so the function is $f(x) = 2(x - 3)(x + 4) = 2x^2 + 2x - 24$.

Provide an Appropriate Response f\mathrm { f }f Having x\mathrm { x }x

Provide an Appropriate Response $\mathrm { f }$ Having $\mathrm { x }$