Question

Amy threw a ball from a height of 5.3 feet. The ball was at a height of 7.3 feet when its horizontal distance from Amy was 2 feet. When it fell to the ground, the ball was 4 feet away from her. Write a quadratic function that models this situation.

Answer 1

The quadratic equation in its generic form is given by:
 y = ax ^ 2 + bx + c
 We must look for the values of a, b and c.
 For this, we have the following points:
 "Amy threw a ball from a height of 5.3 feet":
 (0, 5.3)
 "The ball was at a height of 7.3 feet when its horizontal distance from Amy was 2 feet":
 (2, 7.3)
 "When it fell to the ground, the ball was 4 feet away from her"
 (4, 0)
 Substituting the points we have:

 For (0, 5.3):
 5.3 = a (0) ^ 2 + b (0) + c
 5.3 = c

 For (2, 7.3):
 7.3 = a (2) ^ 2 + b (2) + 5.3
 7.3 = 4a + 2b + 5.3

 For (4, 0):
 0 = a (4) ^ 2 + b (4) + 5.3
 0 = 16a + 4b + 5.3

 We solve the system for a and b:
 7.3 = 4a + 2b + 5.3
 0 = 16a + 4b + 5.3
 Where do we get:
 a = -1.1625
 b = 3,325

 Answer:
 a quadratic function that models this situation is:
 y = -1.1625x ^ 2 + 3.325x + 5.3