Give the focus, directrix, and axis for the parabola.
-If an object is thrown upward with an initial velocity of $12 \mathrm { ft }$ per second, then its height is given by $\mathrm { h } = - 12 \mathrm { t } ^ { 2 } + 48 \mathrm { t }$. What is its maximum height?
A) $72 \mathrm { ft }$
B) $48 \mathrm { ft }$
C) $24 \mathrm { ft }$
D) $36 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height of the parabola can be found by determining the vertex of the quadratic equation $ h = -12t^2 + 48t $. The vertex form of a parabola $ ax^2 + bx + c $ has its vertex at $ t = -\frac{b}{2a} $. Here, $ a = -12 $ and $ b = 48 $, so $ t = -\frac{48}{2(-12)} = 2 $. Substituting $ t = 2 $ back into the equation gives $ h = -12(2)^2 + 48(2) = 48 $ ft. Thus, the maximum height is $ 48 $ ft.

Give the Focus, Directrix, and Axis for the Parabola 12ft12 \mathrm { ft }12ft

Give the Focus, Directrix, and Axis for the Parabola $12 \mathrm { ft }$