Determining the equation of a quadratic function

[Math_Junkie]

What is the equation of the following quadratic function?

I know it's been reflected about the x axis. I believe it's been vertically stretched as well by a factor of 2? It's been translated up and to the left - but I'm having trouble finding the exact formula that would give me this graph. Is there a method to solve this that I'm not seeing? :?

Thanks a bunch.

 

[fasteddie65]

(-2, 2), (0, 1), and (1, -2.5) are on the curve.

y = ax^2 + bx + c
2 = a(-2)^2 + b(-2) + c
1 = a(0)^2 + b(0) + c
-2.5 = a(1)^2 + b(1) + c

2 = 4a - 2b + c
1 = c
-2.5 = a + b + c

This is a system of 3 equations with 3 variables. Many methods can be used to find a, b, and c.

a = -1
b = -2.5
c = 1

The equation is y = -x^2 - 2.5x + 1.