Quadratic Function

A quadratic function is given as f (x) = ax² + bx + c where a, b and c are coefficients. Sometimes, it is also written in the form of f (x) = a(x - h)² + k where (h, k) is the coordinates of the vertex. The graph below shows the quadratic curves in the first form (blue) and the second form (purple). The red dotted curve is the basic form of quadratic equation y = x².


Slide the values of a, b, c, h and k to observe the change of the graph f(x) = ax² + bx + c and f(x) = a(x - h)² + k. Can you get the formulae relating the values of a, b and c with the values of h and k?

Betty, Created with GeoGebra