To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon can use the Zero Product Property. This property states that if a product of factors equals 0, at least one of the factors must also equal 0.
In the equation \(0 = -12x(x - 20)\), Leon can set each factor equal to 0:
- \(-12x = 0\)
- \(x - 20 = 0\)
Now, let's solve these equations:
- From \(-12x = 0\), we can divide both sides by -12 to get \(x = 0\).
- From \(x - 20 = 0\), we can add 20 to both sides to get \(x = 20\).
Thus, the two values of \(x\) are 0 and 20. This means the ball hits the ground at a horizontal distance of 0 (when it is kicked) and at 20 (when it lands).
Therefore, to answer the original question, Leon can use the Zero Product Property to solve the two equations: \(-12x = 0\) and \(x - 20 = 0\).
The correct response is:
Solve the two equations: −12x=0 and x−20=0.