Leon can use 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 ab = 0, then either a = 0 or b = 0.
In this case, the equation 0 = −12x(x−20) can be rewritten as −12x(x−20) = 0.
By applying the Zero Product Property, we can conclude that either -12x = 0 or (x−20) = 0.
To find the horizontal distance the ball has traveled when the height is 0, we need to solve these equations separately.
From -12x = 0, we find that x = 0.
From (x−20) = 0, we find that x = 20.
Therefore, the ball hits the ground at a horizontal distance of 0 or 20 units.
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?
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. 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 . Solve the two equations: −12x=0 and x−20=0.
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