Question

Rowan tosses a ball toward his opponent during a game of table tennis. Function h demonstrates the height of the ball, in meters, when it is a distance x meters away from Rowan.

h(x) = -1/4x^2 + 1/2x + 1/2

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

A.
The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.
B.
The maximum height of the ball is 2.73 meters, which occurs when it is approximately 1 meter away from Rowan.
C.
The maximum height of the ball is 1 meter, which occurs when it is approximately 0.75 of a meter away from Rowan.
D.
The maximum height of the ball is 1 meter, which occurs when it is approximately 2.73 meters away from Rowan.
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Answer 1

A. The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.

Explanation:

To find the maximum point, we find the vertex. In order to do this we must first find the axis of symmetry:

x = -b/2a

In this equation, the value of b is 1/2 and the value of a is -1/4:

`x=(-b)/(2a)\\\\=((-1)/(2))/(2* (-1)/(4))\\\\=((-1)/(2))/((-1)/(2))=1`

This is the x-coordinate of our vertex. Next we substitute this into the function:

h(1) = -1/4(1²)+1/2(1)+1/2)

= -1/4+1/2+1/2

= -1/4+2/4+2/4 = 3/4

This makes the vertex (1, 3/4) or (1, 0.75).

The x-value is the number of meters away the ball is from Rowan and the y-coordinate is the height; this means when the ball is 1 meter away from Rowan, it is 0.75 m in the air.