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
Answers
GPT 3.5
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.
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.