Question

Jackie, who is 5 feet tall, throws a football into the air as if she were throwing it to someone. The path of the football can be expressed by the equation y=−0.05x2+0.75x+5 . Solve as if you were to graph the parabola to figure out how far from Jackie the ball landed

Answer 1

To find out how far from Jackie the ball landed, we need to find the x-coordinate when y=0, because the x-coordinate represents the distance from Jackie where the ball landed.

Setting y=0 and solving for x in the equation y=−0.05x^2+0.75x+5:
0 = -0.05x^2 + 0.75x + 5

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Since factoring may not be straightforward for this equation, let's use the quadratic formula:

x = [-0.75 ± sqrt((0.75)^2 - 4(-0.05)(5))] / 2(-0.05)
x = [-0.75 ± sqrt(0.5625 + 1)] / -0.1
x = [-0.75 ± sqrt(1.5625)] / -0.1
x = [-0.75 ± 1.25] / -0.1

We have two possible solutions for x:
x1 = (-0.75 + 1.25) / -0.1 = 0.5 / -0.1 = -5
x2 = (-0.75 - 1.25) / -0.1 = -2 / -0.1 = 20

Since the ball cannot have landed behind Jackie, we discard the negative solution. Therefore, the ball landed 20 feet from Jackie.