Question

Where x is the horizontal distance in feet from the point at which the ball is thrown.

Answer 1

(a) 5 feet

(b) 19 feet

(c) 30.3 feet

To solve (a):

The initial height will be when x=0, because is in the kids hand. So we take x=0 in the formula:

`y=-(1)/(14)(0)^2+2\cdot0+5=0+0+5=5`

THe height of the ball when leaves the childs hand, is 5 feet. THat's the answer for (a)

To solve (b):

To find how high the ball gets, we need to find the y coordinate of the vertex of the parabolla.

Then, using:

`y-\text{vertex}=-(b)/(2a)`

Then

`-(2)/(2\cdot(-(1)/(14)))=14`

x-coordinate of the vertex is 14. Now to find y-coordinate, we evaluate the function in x=14

`y=-(1)/(14)(14)^2+2\cdot14+5=-14+28+5=19`

The answer to (b) is 19 feet.

To solve (c):

We need to know when the ball hit the ground. That means that y = 0, because y is the height. Then using the quadratic formula:

`\begin{gathered} -\frac{2\pm\sqrt[]{2^2-4\cdot(-(1)/(14))\cdot5}}{2\cdot((-1)/(14))}=14\pm\sqrt[]{266} \\ 14-\sqrt[]{266}=-2.3 \\ 14-\sqrt[]{266}=30.3 \end{gathered}`

One of the results is negative, so it doesn't have sense. The answer to (c) is 30.3 feet