A ball is thrown across a playing field. Its height (in feet) above the ground i

Question

A ball is thrown across a playing field. Its height (in feet) above the ground is given in terms of the horizontal distance x (in feet) that it has traveled: h(x)= -1/12x^2 +x+5
A) what maximum height does the ball reach? Find the maximum height algebraically.
B) what is the horizontal distance traveled when the ball hits the ground? Give an exact value. A ball is thrown across a playing field. Its height (in feet) above the ground is given in terms of the horizontal distance x (in feet) that it has traveled: h(x)= -1/12x^2 +x+5
A) what maximum height does the ball reach? Find the maximum height algebraically.
B) what is the horizontal distance traveled when the ball hits the ground? Give an exact value.
A) what maximum height does the ball reach? Find the maximum height algebraically.
B) what is the horizontal distance traveled when the ball hits the ground? Give an exact value.

Explanation / Answer

A)

The equation:
y = -1/12*x^2 + x + 5
describes a parabola that opens downward (negative coefficient associated with the x^2 term) therefore, finding the vertex will give us the answer.
Axis of symmetry:
x = -b/(2a) = -1/(2*(-1/12)) = 6
Plug the above back into:
y = -1/12*x^2 + x + 5
y = -1/12*(6)^2 + 6 + 5
y = -3 + 6 + 5
y = 8 feet

B)

Set y = 0 and solve for x:
y = -1/12*x^2 + x + 5
0 = -1/12*x^2 + x + 5
Solve using the quadratic formula... doing so yields:
x = {-3.8, 15.8}
We can toss out the negative answer leaving:
x = 15.8 feet

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