Question

How do you graph the function `f(x) = -1/3 (x-2)^2 +3`?

Answer 1

Its graph is a parabola opening downward with vertex `(x,y)=(2,3)`, `y`-intercept `y=5/3`, and `x`-intercepts at `x=-1,5`. You can also plot more points to help you draw the graph.

Explanation:

A quadratic function `f(x)=a(x-h)^2+k` is said to be in vertex form and has vertex (high or low point) at the point `(x,y)=(h,k)`. This will be a low point if `a>0` (the parabola opens upward) and a high point if `a<0` (the parabola opens downward).