The general form of a quadratic function is --> y = ax^2 + bx + c
Since (0, -2) exists for the function, we can plug in those values:
-2 = a(0)^2 + b(0) + c
-2 = 0 + 0 + c
-2 = c
So now our function so far is --> y = ax^2 + bx - 2
We have two pairs of coordinates left: (-1, -8) and (3, -8).
First, plug in the first pair and simplify as much as you can:
-8 = a(-1)2 + b(-1) - 2
-8 = a - b - 2 ( add 2 to both sides )
-6 = a - b (stop here because we can't go further)
Second, plug in the second pair and simplify as much as you can:
-8 = a(3)2 + b(3) - 2
-8 = 9a + 3b - 2 ( add 2 to both sides )
-6 = 9a + 3b (stop here because we can't go further)
Now we have these two equations left:
a - b = -6
9a + 3b = -6
Now we solve for a and b using systems of equations, using one of three ways:
substitution
elimination
graphing (not my favorite, but it is doable)
Using substitution:
a - b = -6 can be rewritten as a = b - 6
plug into the second equation and solve for b
9(b - 6) + 3b = -6 (distribute the 9)
9b - 54 + 3b = -6 (combine all of the b's)
12b - 54 = -6 (add 54 to both sides)
12b = 48 (divide by 12 on both sides to isolate b)
b = 4
plug b into one of the original two equations
a - 4 = -6 (add 4 to both sides)
a = -2
The quadratic equation for this table is y = -2x^2 + 4b - 2