Answer:
Basic parabola: y = ax2 + bx + c
We have 3 points we can plug in for (x, y) to create 3 simultaneous equations
(-2, 24): 24 = 4a - 2b + c {equation 1}
(3, -1): -1 = 9a + 3b + c {equation 2}
(-1, 15): 15 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = 24 {equation 1}
a - b + c = 15 {equation 3}
--------------------- subtract
3a - b = 9
9a + 3b + c = -1 {equation 2}
a - b + c = 15 {equation 3}
-------------------- subtract
8a + 4b = -16
We now have two equations with 2 unknowns we can use to find a, b
3a - b = 9 {equation 4}
8a + 4b = -16 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = 36
8a + 4b = -6
----------------- add
20a = 30
a = 30/20
a = 3/2
8a + 4b = -6
8(3/2) + 4b = -6
12 + 4b = -6
4b = -6- 12
4b = -18
b = -18/4
b = -9/2
Plug these 2 values into one of the original equations and solve for c
15 = a - b + c {equation 3}
15 = 3/2 + 9/2 + c
15 = 12/2 + c
15 = 6 + c
c = 15-6
c = 9
y = (3/2)x2 - (9/2)x+ 9
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