Question

I need the table filled in the graph is it a maximum or minimum and the vertex

Answer 1

Function y=-x²+6x

First you need to start finding the values for y.

When x=0 you will have

`\begin{gathered} y=-x^2+6x \\ f(0)=-0^2+6\cdot0=0 \end{gathered}`

And you have to do the same with the different values as follows:

`\begin{gathered} f(1)=-1^2+6\cdot1=5 \\ f(2)=-2^2+6\cdot2=8 \\ f(3)=-3^2+6\cdot3=9 \\ f(4)=-4^2+6\cdot4=8 \\ f(5)=-5^2^{}+6\cdot5=5 \\ f(6)=-6^2^{}+6\cdot6=0 \end{gathered}`

As you can see in the graph, the function has a maximum in (3,9)

And the vertex is in the same point