To find the parabolic equation that describes the height of the golf ball as it moves away from Lorraine, we can use the vertex form of a parabolic equation:
y = a(x-h)^2 + k
Where (h, k) is the vertex of the parabola. In this case, h represents the horizontal distance from Lorraine, and k represents the maximum height of the golf ball.
Given that the ball is 30 feet in the air at its highest point and lands 60 feet away from Lorraine, we can determine the vertex to be at (30, 30).
So the equation for the height of the golf ball is:
y = a(x-30)^2 + 30
To find the value of a, we can use the point (0, 0) (where Lorraine hits the ball) to solve for a:
0 = a(0-30)^2 + 30
0 = a(900) + 30
-30 = 900a
a = -30/900
a = -1/30
Therefore, the final equation for the height of the golf ball is:
y = -(1/30)(x-30)^2 + 30
To find the height of the golf ball when it is 15 feet away from Lorraine (x=15), we can substitute x=15 into the equation:
y = -(1/30)(15-30)^2 + 30
y = -(1/30)(-15)^2 + 30
y = -(1/30)(225) + 30
y = -225/30 + 30
y = -7.5 + 30
y = 22.5
So, the height of the golf ball when it is 15 feet away from Lorraine is 22.5 feet.
lorraine hits golf ball into the air it lands 60 feet away from her at its highest point the ball is 30 feet in the air find the parabolic equation that describes the height of the ball as it moves away from lorraine use this equation to evaluate the function to answer the following question what is the height of the gold ball when it i 15 feet away from Lorraine
1 answer
1 answer