The path of a soccer ball can be modeled by the equation h(x)=−12x(x−20) , where h(x) is the height of the ball, and x is the horizontal distance the ball has traveled. To determine how far the ball has traveled when it hits the ground, Leon set the height equal to 0 and obtained the equation: 0=−12x(x−20) . How can he use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0?(1 point)
Responses
Plug in 0 for all the x terms in the function.
Plug in 0 for all the x terms in the function.
He cannot use the Zero Product Property because the height will never be 0.
He cannot use the Zero Product Property because the height will never be 0.
Solve the two equations: −12x=0 and x−20=0.
Solve the two equations: negative Start Fraction 1 over 2 End Fraction x equals 0 and x minus 20 equals 0 .
Cancel out the x and then multiply −12 and −20.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .
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To use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon should solve the two equations: −12x = 0 and x − 20 = 0.
The Zero Product Property states that if the product of two numbers is zero, then at least one of the numbers must be zero. In this case, the product is −12x(x − 20). If this product equals zero, then either −12x equals zero or (x − 20) equals zero.
By solving each equation, Leon can find the possible values for x that would make h(x) equal to zero. The solutions will tell him the horizontal distances at which the ball is at the ground level.
For −12x = 0, the solution is x = 0. This represents the starting point where the ball has not traveled any horizontal distance.
For x − 20 = 0, the solution is x = 20. This represents the horizontal distance the ball has traveled when it hits the ground again after being kicked.
In conclusion, the ball starts at a horizontal distance of 0 and hits the ground after traveling 20 units of horizontal distance.