Finding a Quadratic Function from a Graph

Choose a form using the intercepts or turning point. Substitute another point to find the scale factor. Quadratics with the same roots can have different values of a. Choosing a form **Given on the graph** | **Start with** | **Then** x-intercepts p and q | y=a(x-p)(x-q) | Substitute one more point to find a Turning point (h,k) | y=a(x-h)2+k | Substitute one more point to find a Example **Given** | **Working** Turning point (2,3), passes through (0,11) | y=a(x-2)2+3 11=a(0-2)2+3 4a=8 a=2 y=2(x-2)2+3 Use a point that gives new information, rather than an intercept or turning point already used.