The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Equation of parabola: $f ( x ) = 8 x ^ { 2 } + 32 x - 12$; associated equation: $0 = 16 x + 32$
A) $( - 2 , - 44 )$
B) $( 2,84 )$
C) $( - 2,84 )$
D) $( 2 , - 44 )$

Question

Quizplus · Accepted Answer

The associated equation $0 = 16x + 32$ is derived from taking the derivative of the parabola's equation $f(x) = 8x^2 + 32x - 12$ and setting it equal to zero to find the x-coordinate of the vertex. Solving $16x + 32 = 0$ gives $x = -2$. Substituting $x = -2$ into the original equation gives $f(-2) = 8(-2)^2 + 32(-2) - 12 = 32 - 64 - 12 = -44$. Therefore, the vertex is $(-2, -44)$.

The Vertex of a Parabola Occurs Where the Derivative of Its