Answer: y = -4x^2 + 4x - 3 which is choice A
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Explanation:
We'll use the template y = ax^2 + bx + c to help find the equation
Plug in x = 0 and y =-3 which is from the point (0,-3)
y = ax^2 + bx + c
-3 = a(0)^2 + b(0) + c
c = -3
Plug in x = -1, y = -11 which is from the point (-1,-11). Also plug in c = -3
y = ax^2 + bx + c
-11 = a(-1)^2 + b(-1) + (-3)
-11 = a - b - 3
a-b = -11+3
a-b = -8
a = b-8 <<-- we'll use this later
Plug in x = 3, y = -27 which is from the point (3,-27). Also plug in c = -3
y = ax^2 + bx + c
-27 = a(3)^2 + b(3) + (-3)
-27 = 9a + 3b - 3
9a + 3b = -27+3
9a + 3b = -24
9(b-8) + 3b = -24 ... replace a with b-8 (works because a = b-8)
9b-72 + 3b = -24
12b-72 = -24
12b = -24+72
12b = 48
b = 48/12
b = 4
Use this b value to find 'a'
a = b-8
a = 4-8
a = -4
So we have
a = -4, b = 4, c = -3
This leads to the equation y = -4x^2 + 4x - 3 which is choice A
You can check the answer by plugging each point into the equation. You should get a true statement each time.
Example: plug in (0,-3)
y = -4x^2 + 4x - 3
-3 = -4(0)^2 + 4(0) - 3
-3 = -3
I'll let you check the others.
