Can someone help me find the vertex, axis of symmetry, maximum/minimum value, and the range of this standard form quadratic function?

Question

kris2015 · Answer

$$y=-x ^{2}+2x+1$$

lyss · Answer

Hi, 

for this equation: y=−x^2+2x+1 
to find the vertex, follow the rule b/2a 
2x/2(x)  or -2x/2(-x), which is equal to 1. 
the x value is 1, and to find the y value, plug x=1 into the original equation. 
y=(1-1)^2+2  = 2 
so x=1 and y=2,  making the vertex (1,2) 

the axis of symmetry is equal to the x value, meaning x=1 
that also means that the max/min value is 1 

and since d (domain) is $$d=-\infty,\infty $$
that means with the y value, the range is $$r=-\infty,2$$