Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the parabolic equation that describes the height of the golf ball as it moves away from Lorraine, we can use the standard form of a parabolic equation:

y = ax^2 + bx + c

First, we need to find the values of a, b, and c. We know that the vertex of the parabola is (0, 30) and that the parabola passes through the point (60, 0). The vertex form of a parabola is y = a(x-h)^2 + k, where (h, k) is the vertex. So, we have:

30 = a(0-0)^2 + 30
30 = 30a
a = 1

Now, we can plug in the values of a and the point (60, 0) into the equation to solve for b and c:

0 = 1(60)^2 + 60b + c
0 = 3600 + 60b + c

Also, the parabola passes through the point (15, ?) we have another equation:

y = 1(15)^2 + 15b + c

Simplifying the equation system:

0 = 3600 + 60b + c
c = 3600 + 60b

Substitute c in the first system:

0 = 3600 + 60b + 3600 + 60b
0 = 7200 + 120b
b = -60

Now, we substitute the values of a, b, and c back into the standard form of the parabola:

y = x^2 - 60x + 3600

To find the height of the golf ball when it is 15 feet away from Lorraine:

y = (15)^2 - 60(15) + 3600
y = 225 - 900 + 3600
y = 2925

Therefore, the height of the golf ball when it is 15 feet away from Lorraine is 2925 feet.