The path of a ball kicked from the ground can be modeled by the equation y=−1/4(x−2)(x−22), where x and y are measured in feet. The x-axis represents the ground. How far does the ball land from where it is kicked?
The problem is to find the two zeros of the function and then find the distance between them.
First: multiply out the equation: y = -0.25(x - 2)(x - 22) = -0.25(x2 - 24x + 44)
Second: set this equation to zero and solve: 0.25(x2 - 24x + 44) = 0
Divide both sides by 0.25: x2 - 24x + 44 = 0
Factor: (x - 2)(x - 22) = 0
Find the zeros: x = 2 or x = 22
Third: find the distance between these two answers: (your turn)