To begin a football game, a kicker has to kick off. The football follows the path h(x)=−130x(x−61) , where h(x) is the height of the football and x is the horizontal distance it has traveled in yards. Solve the equation to determine how far the ball will have traveled when it hits the ground. 0=−130x(x−61)
To determine how far the ball will have traveled when it hits the ground, we set h(x) equal to 0 and solve for x.
0 = -130x(x - 61)
Since x cannot be equal to 0 (since this would mean the ball hasn't traveled any horizontal distance), we can divide both sides of the equation by -130 to simplify it:
0 = x(x - 61)
Now we can solve for x by setting each factor equal to zero:
x = 0 or x - 61 = 0
For x = 0, the ball would not have traveled any horizontal distance and would be at the starting point, so we discard this solution.
For x - 61 = 0, we solve for x:
x = 61
Therefore, the ball will have traveled 61 yards when it hits the ground.
To determine how far the ball will have traveled when it hits the ground, we need to find the value of x when h(x) is equal to zero.
Given the equation:
0 = -130x(x - 61)
To solve this equation, we can use the zero-product property, which states that if a * b = 0, then either a = 0 or b = 0.
In this case, we have two factors: x and (x - 61). Therefore, either x = 0 or (x - 61) = 0.
Setting x - 61 = 0, we find:
x = 61
So, the ball will have traveled 61 yards when it hits the ground.
To solve the equation and determine how far the football will have traveled when it hits the ground, we need to find the value of x when the height h(x) is equal to zero.
The given equation is:
0 = -130x(x - 61)
To solve this equation, we can set each factor equal to zero and solve for x individually:
Setting the first factor equal to zero:
-130x = 0
x = 0
Setting the second factor equal to zero:
x - 61 = 0
x = 61
So we have two possible values for x: 0 and 61.
To determine which value corresponds to when the ball hits the ground, we need to consider the context of the problem. In this case, the ball is being kicked off, which means it starts at ground level. Therefore, x = 0 represents the starting point of the ball, not the distance it has traveled when it hits the ground.
Thus, the correct value for x when the ball hits the ground is x = 61.
Therefore, the ball will have traveled 61 yards when it hits the ground.