Notice that represents a quadratic function
and its graph is a parabola with vertex (*h*,*k*).

- Let
*f*(*x*)=-3(*x*-3)^{2}+4, then- find its vertex, [Vertex is (3,4) ].
- find its
*y*-*intercept*, [*y*-*intercept*is - find its
*x*-*intercep*(*s*), [ set*y*=0, we get -3(*x*-3)^{2}+4=0, this is equivalent to 3(*x*-3)^{2}=4 or so - sketch the graph of
*f*. [Use Maple syntax to plot*f*.]

- Let Then solve the problems mentioned above.
- Find the quadratic function
*f*(*x*) which has the vertex (-2,3) and the graph of*f*passes through (2,0). [Consider the function since vertex is (-2,3), we can write*f*(*x*)=*a*(*x*+2)^{2}+3. Now*y*=*f*(*x*) passes through (2,0), so substitute*x*=2, and*y*=0,*i*.*e*. so Therefore, the function we need is (you can use Maple to check if your graph looks right). - Find the quadratic function
*f*(*x*) which has the vertex (2,-3) and the graph of*f*passes through (1,1). - Find the quadratic function
*f*(*x*) which has the vertex (1,3) and the graph of*f*passes through (-2,-3).