Answer:
A. The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.
Step-by-step 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:
[tex]x=\frac{-b}{2a}\\\\=\frac{\frac{-1}{2}}{2\times \frac{-1}{4}}\\\\=\frac{\frac{-1}{2}}{\frac{-1}{2}}=1[/tex]
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.
