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Parabola

It’s possible to find the function of a parabola, if three of its points are given:
(x_1,y_1)(x_2,y_2)(x_3,y_3)

There are two ways to do that:

You can either solve three equations with tree unknowns. You get the three equations simply by substituting the three different values of x and y into the quadratic function: y=a*x^2+b*x+c.


y_1=a*x_1^2+b*x_1+c

y_2=a*x_2^2+b*x_2+c

y_3=a*x_3^2+b*x_3+c


Or you can use the formula:

y=frac{(x-x_2)*(x-x_3)}{(x_1-x_2)*(x_1-x_3)}*y_1+frac{(x-x_1)*(x-x_3)}{(x_2-x_1)*(x_2-x_3)}*y_2+frac{(x-x_1)*(x-x_2)}{(x_3-x_1)*(x_3-x_2)}*y_3