Question

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

Answer 1

\[y=-x ^{2}+2x+1\]

Answer 2

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 \[r=-\infty,2\]