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.
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.
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 needs to set the equation he obtained, 0 = -12x(x-20), equal to 0 and solve for x.
So, Leon would set the equation equal to zero, like this: -12x(x-20) = 0.
Then, he can use the Zero Product Property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
Therefore, by setting each factor equal to zero, Leon can solve for x. He would solve the equations -12x = 0 and x-20 = 0 separately to find the possible values for x.
Once he solves these equations, he will find the solutions, which represent the horizontal distance(s) the ball has traveled when the height is zero.
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 needs to set the equation h(x) equal to 0: 0 = -12x(x-20).
To apply the Zero Product Property, he needs to break down the equation into two separate factors and set each factor equal to zero. In this case, the two factors are -12x and (x-20). So, he will set each factor equal to zero and solve for x:
1) -12x = 0
Divide both sides of the equation by -12, and he gets x = 0.
2) x - 20 = 0
Add 20 to both sides of the equation, and he gets x = 20.
Therefore, the two solutions for x are x = 0 and x = 20. These indicate the horizontal distances at which the soccer ball hits the ground.
So, when the height of the soccer ball equals 0, the horizontal distance the ball has traveled can be found at x = 0 and x = 20.