Question 18324
there are 2 ways to solve, graph or mathematical.
the graph would look like this
{{{graph(500,500,-10,10,-10,10,x^2-6x)}}}
If your graph was super detailed, you could see where the bottom was, but we can't here.  Well, we can, but it's not accurate, so we use a formula to check.
The vertex is the very bottom of the little dip.
A formula would be
{{{h=b/-2a}}}
H stands for the X value of the vertex
K stands for the Y value of the vertex
The b is in {{{ax^2+bx+c=0}}}
In this case, the b would be -6 and the a woul dbe 1
Plug the numbers into the formula
{{{h=-6/-2(1)}}}
{{{h=3}}}
The X value of the vertex is 3, as stated in your answer key. :)

Then to find the Y value, plug 3 into wherever you see X.
{{{(3)^2-6(3)}}}
{{{9-18=-9}}}
The Y value of the vertex is -9, as stated in your answer key :)
So, the vertex is (3,-9)

In this case, you can clearly see what the X-intercepts are.
(0,0) and (0,6)
Hope this helps!