Answer:
f(x) = 4x^2 + 2x - 4.
Step-by-step explanation:
Let the quadratic function be y = f(x) = ax^2 + bx + c.
For the point (-2, 8) ( x = -2 when y = 8) we have:
a(-2)^2 + (-2)b + c = 8
4a - 2b + c = 8 For (0, -4) we have:
0 + 0 + c = -4 so c = -4. For (4, 68) we have:
16a + 4b + c = 68
So we have 2 systems of equations in a and b ( plugging in c = -4):
4a - 2b - 4 = 8
16a + 4b - 4 = 68
4a - 2b = 12
16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:
8a - 4b = 24
Adding the last 2 equations:
24a = 96
a = 4
Now plugging a = 4 and c = -4 in the first equation:
4(4) - 2b - 4 = 8
-2b = 8 - 16 + 4 = -4
b = 2.
