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)%0D%0AResponses%0D%0A%0D%0APlug in 0 for all the x terms in the function.%0D%0APlug in 0 for all the x terms in the function.%0D%0A%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0A%0D%0ASolve the two equations: −12x=0 and x−20=0.%0D%0ASolve the two equations: negative Start Fraction 1 over 2 End Fraction x equals 0 and x minus 20 equals 0 .%0D%0A%0D%0ACancel out the x and then multiply −12 and −20.%0D%0ACancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0Apage 18 of 18

Question

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)%0D%0AResponses%0D%0A%0D%0APlug in 0 for all the x terms in the function.%0D%0APlug in 0 for all the x  terms in the function.%0D%0A%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0A%0D%0ASolve the two equations: −12x=0 and x−20=0.%0D%0ASolve the two equations:  negative Start Fraction 1 over 2 End Fraction x equals 0  and  x minus 20 equals 0 .%0D%0A%0D%0ACancel out the x and then multiply −12 and −20.%0D%0ACancel out the x and then multiply  negative Start Fraction 1 over 2 End Fraction  and  negative 20 .%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0Apage 18 of 18

GPT-4 Turbo · Answer

Leon can apply the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0. The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero.

The given equation is: 0 = −12x(x − 20)

To use the Zero Product Property, Leon needs to set each factor equal to zero and solve for the variable x:

−12x = 0 and x − 20 = 0

For the first equation, −12x = 0, we can divide by −12 (which doesn't actually change anything since any number times zero is still zero), yielding:

x = 0

For the second equation, x − 20 = 0, we add 20 to each side to isolate x:

x = 20

So, by setting the factors equal to zero and solving for x, Leon finds the two horizontal distances at which the height of the soccer ball is 0: one at the initial position x = 0 where the ball is kicked, and one at x = 20, which is the distance the ball has traveled horizontally when it hits the ground. Hence, the soccer ball has traveled 20 units of horizontal distance when it reaches the ground.