How do I find a quadratic function given some points?

Question

Like, for linear functions you can just find the slope and b to find the function. How do you do this for quadratic functions?

Answer 1

It is possible, though sometimes complicated, as long as you are given 3 points. Quadratic functions are in the form y = ax^2 + bx + c. Note that there are 3 unknowns namely a, b, and c.

The way that you would do it is to plug each point into the function, put the x coordinate in place of x and the y coordinate in place of y. This will give you an equation. Repeat for the other two points so that you end up with 3 equations.

Now, solve the system of equations for a, b, and c and you have it!

Answer 2

Quadratic equations are always parabolas. Without more information, just knowing a few point on the plane may not be sufficient to define a unique parabola: you need to know the position of the focus and vertex (or vertex and directrix) to map the quadratic.