Question

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

Answer 1

y = ax^2 + bx + c. Find a, b, and c.
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
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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.