Question
The path of a soccer ball can be modeled by the equation h(x)=−1/2x(x−20)
, where h(x)
is the height reached by the ball, in feet, and x is the horizontal distance the ball has traveled, in feet. What is the horizontal distance the ball will have traveled when it hits the ground? Use a graph or table if necessary.(1 point)
The ball will have traveled a horizontal distance of
feet when it hits the ground.
, where h(x)
is the height reached by the ball, in feet, and x is the horizontal distance the ball has traveled, in feet. What is the horizontal distance the ball will have traveled when it hits the ground? Use a graph or table if necessary.(1 point)
The ball will have traveled a horizontal distance of
feet when it hits the ground.
Answers
GPT-4o mini
To determine the horizontal distance the ball will have traveled when it hits the ground, we need to find the value of \( x \) when the height \( h(x) \) is equal to 0. This means we need to solve the equation:
\[
h(x) = -\frac{1}{2}x(x - 20) = 0
\]
We can factor the equation:
\[
-\frac{1}{2}x(x - 20) = 0
\]
Setting each factor equal to zero gives us:
1. \( -\frac{1}{2} = 0 \) (not possible)
2. \( x = 0 \)
3. \( x - 20 = 0 \) which leads to \( x = 20 \)
Thus, the solutions to the equation are \( x = 0 \) and \( x = 20 \).
The value \( x = 0 \) corresponds to the initial point when the ball is kicked. The value \( x = 20 \) corresponds to the horizontal distance when the ball hits the ground.
So, the horizontal distance the ball will have traveled when it hits the ground is **20 feet**.
\[
h(x) = -\frac{1}{2}x(x - 20) = 0
\]
We can factor the equation:
\[
-\frac{1}{2}x(x - 20) = 0
\]
Setting each factor equal to zero gives us:
1. \( -\frac{1}{2} = 0 \) (not possible)
2. \( x = 0 \)
3. \( x - 20 = 0 \) which leads to \( x = 20 \)
Thus, the solutions to the equation are \( x = 0 \) and \( x = 20 \).
The value \( x = 0 \) corresponds to the initial point when the ball is kicked. The value \( x = 20 \) corresponds to the horizontal distance when the ball hits the ground.
So, the horizontal distance the ball will have traveled when it hits the ground is **20 feet**.