find two points on the graph of the parabola other than the vertex and x-intercept

Question

r(x)=-x^2+2x , i need help to see what points are going through this without using the stuff(what i mentioned in my question) my vertex is (1,1) and the x-intercepsts is (2,0),(0,0) . What are two other points on the graph

Answer 1

try x=-2.

r(-2) = - (-2)^2 + 2(-2) = -4 + -4 = -8

so (-2,-8) is also on the graph of the parabola

From the vertex, it is 9 units down and 3 to the left.

So the reflection is 9 units down and 3 to the right.

That is (4,-8)

Note that r(4) = -4^2 + 2(4) = -16 + 8 = -8

so now your table looks like this:

x y

1 1 <--- vertexx

0 0 <--- solution

2 0 <--- solution

-2 -8

4 -8

now you can get a pretty good graph