Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?
The equation for a parabola would be knowing the values of in .
What does C = (-2,7) on the parabola tell you? It says that when x = -2, the y value of that formula will be 7.
Thus .
So C on the parabola tells you that .
A and B on the parabola will likewise tell you something. And if you know what a, b, and c are, then you have "found the parabola".
Let:
From the given points, this gives the 3X3 linear system:
Simplified:
this allows us to reduce the problem to the following 2X2 system
Solve this system, and you will have the values of the coefficients which will give you the parabola you want.