Answer:
y = x² +10x -9
Explanation:
A spreadsheet or suitable calculator can help you with this. All spreadsheets and most graphing calculators offer regression function capabilities. It is a good idea to learn to use these tools.
The attached graphing calculator output shows the equation to be ...
y = x² +10x -9
_____
Additional comment
If you want to do this by hand, you recognize that there are only two coefficient values that need to be found. You can choose any two of the given points to use to create equations for those coefficients. I would choose the points with the x-values that are smallest in magnitude.
Using (-4, -33)
y = x² +bx +c
-33 = (-4)² +(-4)b +c
-4b +c = -49 . . . . . . . . . subtract 16
Using (1, 2)
2 = (1)² +(1)b +c
b +c = 1 . . . . . . . . . . . . subtract 1
Now, we can subtract the first equation from the second ...
(b +c) -(-4b +c) = (1) -(-49)
5b = 50 . . . . . . . . simplify
b = 10 . . . . . . . . . . divide by 5
Using the second equation, we get
10 +c = 1
c = -9 . . . . . . subtract 10
So, the desired quadratic is ...
y = x² +10x -9
__
These equations are usually pretty easy to solve, because the 'c' variable has a coefficient of 1 in all of them. It can easily be eliminated by subtracting one equation from another. Here, we chose our subtraction so the coefficient of 'b' would end up being positive. (Not necessary, but can help prevent mistakes.)
If you don't know ahead of time that the coefficient of x² is 1, then you need to write 3 equations in the three coefficients.