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.
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 .
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.
The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero. For the equation given:
0 = -12x(x - 20)
The two factors are -12x and (x - 20). According to the Zero Product Property, we set each factor equal to zero and solve for x:
For -12x:
-12x = 0
Divide both sides by -12 to isolate x:
x = 0
For (x - 20):
x - 20 = 0
Add 20 to both sides to solve for x:
x = 20
Therefore, by using the Zero Product Property, Leon can conclude that the horizontal distances at which the height of the soccer ball equals 0 are 0 and 20 units. This means the ball starts at ground level (when x = 0), reaches its peak, and then hits the ground again after traveling a horizontal distance of 20 units (when x = 20).
so it is c
My apologies for any confusion, but the correct application of the Zero Product Property in this case is option (b):
"Solve the two equations: −12x = 0 and x−20 = 0."
Leon needs to solve these two separate equations to find the values of x when the height of the ball, h(x), equals zero. By doing this, he will find the horizontal distances where the ball is on the ground:
For −12x = 0, solving for x gives x = 0.
For x - 20 = 0, solving for x gives x = 20.
The horizontal distances the ball has traveled when the height is zero are at x = 0 (where the ball is kicked) and at x = 20 (where the ball lands).
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 a product of factors is equal to zero, then at least one of the factors must be zero.
In this case, Leon needs to set the equation 0=−12x(x−20) equal to zero. He can do this by multiplying out the equation:
0=−12x(x−20)
0=−12x^2 + 240x
Now, using the Zero Product Property, he can set each factor equal to zero and solve for x:
−12x^2 + 240x = 0
−12x(x − 20) = 0
Setting the first factor equal to zero:
−12x = 0
x = 0
Setting the second factor equal to zero:
x − 20 = 0
x = 20
Therefore, the horizontal distance the ball has traveled when the height of the soccer ball equals 0 is x = 0 or x = 20.