SOLUTION: A ball is thrown across a playing field. Its path is given by the equation y=-0.005x^2+x+5. Where x is the distance the ball has traveled horizontally and y is its height above gro

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Question 317230: A ball is thrown across a playing field. Its path is given by the equation y=-0.005x^2+x+5. Where x is the distance the ball has traveled horizontally and y is its height above ground level, both measured in feet.
a. What is the maximum height attained by the ball?
b. How far has it traveled horizontally when it hits the ground?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
A ball is thrown across a playing field. Its path is given by the equation y=-0.005x^2+x+5. Where x is the distance the ball has traveled horizontally and y is its height above ground level, both measured in feet.
a. What is the maximum height attained by the ball?
The equation:
y=-0.005x^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*(-0.005)) = 100
Plug the above back into:
y=-0.005x^2+x+5
y=-0.005(100)^2+100+5
y = -50+100+5
y = 55 feet
.
b. How far has it traveled horizontally when it hits the ground?
Set y=0 and solve for x:
y=-0.005x^2+x+5
0=-0.005x^2+x+5
Solve using the quadratic formula... doing so yields:
x = {-4.88, 204.88}
We can toss out the negative answer leaving:
x = 204.88 feet
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1.1 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -4.88088481701516, 204.880884817015. Here's your graph:

.