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

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

And the positive solution is

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

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents