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Find the quadratic function that has a vertex at (-1,3) and whose graph passes through the point (2,1).
All quadratic functions are in the form
or for convenience, let's write for
where the vertex is (,).
So since the vertex is (,), we plug those in
Now all we need is
So we substitute (,) = (,).
in functional notation.
To draw the graph, plot the given vertex and the given
point, and find some more points, say:
(-7,-5), (-4,1), (5,-5)
Now draw in the graph of the function: