The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 144 feet per second is a function of the time and is given by the equation f ( x ) = 144 x $-$ 16 x 2 , where x represents the time. Find the highest point reached by the projectile.
A) 144 feet
B) 324 feet
C) 648 feet

Question

Quizplus · Accepted Answer

To find the highest point reached by the projectile, we need to find the vertex of the parabola represented by the function f(x). The x-coordinate of the vertex is given by:
x = -b / 2a
where a = -16 and b = 144. Substituting the values, we get:
x = -144 / 2(-16) = 4.5
So, the highest point is reached after 4.5 seconds. Substituting this value back into the function, we get:
f(4.5) = 144(4.5) - 16(4.5)^2 = 324
Therefore, the highest point reached by the projectile is 324 feet.

The Height of a Projectile Fired Vertically into the Air −-−

The Height of a Projectile Fired Vertically into the Air $-$