Solve the problem.
-An arrow is fired into the air with an initial velocity of 128 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = -16t2 + 128t. Find the maximum height of the arrow.
A) 256 ft
B) 64 ft
C) 768 ft
D) 448 ft

Question

Quizplus · Accepted Answer

The maximum height of the arrow can be found by using the vertex formula for a parabolic equation of the form $h(t) = at^2 + bt + c$. The time at which the maximum height is reached is given by $t = -\frac{b}{2a}$. In this case, $a = -16$ and $b = 128$, so $t = -\frac{128}{2(-16)} = 4$. Plugging this back into the equation for $h$, we get $h(4) = -16(4)^2 + 128(4) = -16(16) + 512 = 256$. Therefore, the maximum height is 256 feet.

Solve the Problem. -An Arrow Is Fired into the Air with an Initial