How to determine the quadratic function from the given graph?

The lesson describes how to get the quadratic function form the given graph of a quadratic function. The graph of y = ax^{2} + bx + c pass through three points (1, 3), (-2, 0)
and (-1, -1), find the quadratic function of this graph.

Any point (x, y) on the graph will satisfy the function y = ax^{2} + bx + c. so we substitute the three points into the function to get three equations.

substitute the point (1, 3) in to the function y = ax^{2} + bx + c, we get 3 = a(1)^{2} + b(1) + c, which simplify to, a + b + c = 3, we name this as equation 1

substitute the point (-2, 0) in to the function y = ax^{2} + bx + c, we get 0 = a(-2)^{2} + b(-2) + c, which simplify to, 4a - 2b + c = 0, we name this as equation 2

substitute the point (-1, -1) in to the function y = ax^{2} + bx + c, we get -1 = a(-1)^{2} + b(-1) + c, which simplify to, a - b + c = -1, we name this as equation 3

We need to solve the three variables one-degree equation to get the coefficient a, b and c, then we can write the quadratic function.