Answer: OPTION A.
Step-by-step explanation:
Given the following function:
![h(x)=-\frac{1}{4}x^2+\frac{1}{2}x+\frac{1}{2}](https://tex.z-dn.net/?f=h%28x%29%3D-%5Cfrac%7B1%7D%7B4%7Dx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B2%7D)
You know that it represents the the height of the ball (in meters) when it is a distance "x" meters away from Rowan.
Since it is a Quadratic function its graph is parabola.
So, the maximum point of the graph modeling the height of the ball is the Vertex of the parabola.
You can find the x-coordinate of the Vertex with this formula:
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
In this case:
![a=-\frac{1}{4}\\\\b=\frac{1}{2}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B1%7D%7B2%7D)
Then, substituting values, you get:
![x=\frac{-\frac{1}{2}}{(2)(-\frac{1}{4}))}\\\\x=1](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%282%29%28-%5Cfrac%7B1%7D%7B4%7D%29%29%7D%5C%5C%5C%5Cx%3D1)
Finally, substitute the value of "x" into the function in order to get the y-coordinate of the Vertex:
Therefore, you can conclude that:
<em> The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.</em>