The path of a projectile launched from a 16-ft-tall tower
is modeled by the equation
y = −16x2 + 64x + 16. Graph the
equation. What is the maximum
height, in feet, reached by the
projectile?
(On a graph)

The maximum height reached by the projectile is 80 feet

Step-by-step explanation:

The given equation of the path of the projectile is y = -16·x² + 64·x + 16

Where;

y = The height in feet, reached by the projectile (Assumption)

x = The time it takes the projectile to reach the height, y (Assumption)

The shape of the given equation of the path of the parabola is that of a parabola turned upside down.

We have that the maximum height is given by the top of the curve where the curve changes direction, and the slope = 0

Therefore, we have;

Therefore, at the maximum point, the slope is -32·x + 64 = 0

∴ x = -64/(-32) = 2 at the maximum point

The height at the maximum point = The maximum height, , is found by finding the value of y (the height) at x = 2 (the value of x at the maximum point)

Therefore, we have;

= -16 × 2² + 64 × 2 + 16 = 80 feet

The maximum height reached by the projectile, = 80 feet.

oof

step-by-step explanation: