Question

The height

y

(in feet) of a ball thrown by a child is

y

=

−

1/14

x2

+

6x

+

3


where

x

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


(a) How high is the ball when it leaves the child's hand?

3

Correct feet


(b) What is the maximum height of the ball?

129

Correct feet


(c) How far from the child does the ball strike the ground? ___ feet


I just need c answered , the rest. is correct

Answer 1

The ball describes a parabola, as you can see in the attached picture. So, the point where the ball strike the ground is the point where the parabola meets the x axis. In fact, the x-axis is the set of points where y=0, which means that the ball has height 0 or -again- it hits the ground.

So, we have to set y=0 in our equation and look for the positive solution. We have

$-\dfrac{1}{14}x^2+6x+3=0 \iff x=42\pm\sqrt{1806}$

And the positive solution is

$42+\sqrt{1806}$

So that's the distance from the child where the ball strikes the ground.