# How to find the formula of a quadratic function knowing that it contains the points (-2,2) and (0,1) and (1,-2.5)?

##### 1 Answer

Apr 18, 2015

Write that this graph passes at the 3 points: (-2, 2); (0, 1) and (1, -2.5).

2 = 4a - 2b + c

1 = c

-2.5 = a + b + c

Solve this system of linear equations.

First c = 1 -->1 = 4a - 2b --> 4a - 2b = 1

-3.5 = a + b --> 2a + 2b = -7

-----------------

6a = -6 --> a = -1

a + b = -3.5 --> b = -3.5 + 1 = -2.5.

Finally the quadratic function is : y = -x^2 -2.5*x + 1

Check:

x = -2 --> y = -4 + 5 + 1 = 2 Correct

x = 1 --> y = -1 - 2.5 + 1 = 2.5. Correct.