SOLUTION: Could you please help with this word problem for a quadratic function? The height h (in feet) of a water balloon can be modeled by h(x) = -3x^2 + 24x + 11, where x is the horizo

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Question 1192394: Could you please help with this word problem for a quadratic function?
The height h (in feet) of a water balloon can be modeled by h(x) = -3x^2 + 24x + 11, where x is the horizontal distance (in feet) from the launch pad.
The launchpad is adjusted so that the water balloon lands exactly 9 feet away from the launchpad. Write a function that models the new path of the water balloon.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The height h (in feet) of a water balloon can be modeled by h(x) = -3x^2 + 24x + 11, where x is the horizontal distance (in feet) from the launch pad.
The launchpad is adjusted so that the water balloon lands exactly 9 feet away from the launchpad.
Write a function that models the new path of the water balloon.
:
We should be able to do this by changing the coefficient of x^2 of the given equation:
x=9, y=0
a*(9^2) + 24(9) + 11 = 0
81a + 216 + 11 = 0
81a = -227
a = -227/81
a = -2.802
new equation
h(x) = -2.802x^2 + 24x + 11

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The coefficient of x^2 depends on the force of gravity.

The coefficient of x is determined by the initial vertical velocity.

The constant term is determined by the initial height.

When the problem says the launchpad is adjusted, it means we are adjusting the initial height -- we are not changing the force of gravity or the initial velocity.

So we need to find the value of c in the function for which the height is 0 at x=9:

ANSWER: After the (height of) the launchpad is adjusted, the function that models the path of the water balloon (as a function of the horizontal distance from the launch pad) is .