Question

graph and label the vertex and y intercept of g(x)=-(x-2)^2+3

Answer 1

this is in the form y=A(x-h)^2+k, where (h,k) is the vertex. since A is negative this parabola opens downward, the vertex is (2,3).
setting y=0 you get:
0=-(x-2)^2+3
(x-2)^2=3
x-2=+/-sqrt(3)
x=+/-sqrt(3)+2 theses are the roots, when y=0