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