To find the parabolic equation that describes the height of the golf ball as it moves away from Lorraine, we first need to find the equation in vertex form.
The vertex form of a parabolic equation is given by: y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
Given that at its highest point, the ball is 30 feet in the air (height = 30) and lands 60 feet away from Lorraine (horizontal distance = 60), we can determine the vertex of the parabola.
The vertex of the parabola is at (h,k) = (30, 30). Substituting these values into the vertex form of the parabola, we get:
y = a(x-30)^2 + 30
Next, we can use the point (0,0) to find the value of 'a':
0 = a(0-30)^2 + 30
0 = 900a + 30
900a = -30
a = -30/900
a = -1/30
Therefore, the equation that describes the height of the golf ball as it moves away from Lorraine 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 = -7.5 + 30
y = 22.5
Therefore, the height of the golf ball when it is 15 feet away from Lorraine is 22.5 feet.
Lorraine hits a 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 golf ball when it is 15 feet away from Lorraine?(1 point) ? feet
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