If the quadratic function has roots of 6 and 10, then the graph of the quadratic must include both (6,0) and (10,0). Furthermore, if the vertex of the graph is the point (8, 2), then the point (8, 2) must also be on the graph.
If a point is on the graph of an equation, then if you substitute the -coordinate value of the point into the function in place of , the result will be that the function value will be the -coordinate of the point.
We are looking for a quadratic function of the form:
Using the coordinate values from the three given points we can write:
Simplifying:
Solve the system for the ordered triple which will give you the coefficients for your function (I recommend the elimination method):
