Question

Daniel hits a golf ball off the tee. The function h demonstrates the height of the ball, in feet, t seconds after it is hit.

h(t)= -16t^2+148t+1/10

Select the statement that accurately describes the maximum point of the graph modeling the height of the golf ball.

A.
The maximum height of the ball is about 342 feet, which occurs approximately 4½ seconds after the ball is hit.
B.
The maximum height of the ball is about 416 feet, which occurs approximately 6½ seconds after the ball is hit.
C.
The maximum height of the ball is about 336 feet, which occurs approximately 4 seconds after the ball is hit.
D.
The maximum height of the ball is about 148 feet, which occurs approximately 8 seconds after the ball is hit.

Answer 1

Answer:

A.  The maximum height of the ball is about 342 feet, which occurs approximately 4½ seconds after the ball is hit.

Step-by-step explanation:

The height of the ball is demonstrated by the equation:

$h(t)=-16t^{2}+148t+\frac{1}{10}$

The given equation is a quadratic equation. The maximum/minimum of a quadratic equation occurs at the vertex.

The vertex of a general quadratic equation of the form:

$ax^{2}+bx+c$

occurs at x =$\frac{-b}{2a}$

Comparing the given equation with general equation, we get:

a = -16

b = 148

So, the maximum value will occur when t will be:

$t=\frac{-148}{2(-16)}=4.625$

From the given options we can see that the closest to 4.625 is 4 $\frac{1}{2}$  which is given by option A.

So from here we can conclude that : The maximum height of the ball is about 342 feet, which occurs approximately 4½ seconds after the ball is hit.

Answer 2

The time is equal to -b /2a

where a is the first number and b is the second number in the given equation.

Time = - 148 / 2(-16) = 4.6 seconds.

Now you can replace t with 4.6 to find the height:

h(t) = -16(4.6)^2 + 148(4.6) +1/10 = 342.4 feet.

Based on t and height.

The answer would be A.