SOLUTION: f(x)= -(x+3)(x+3)+3 Please help me find the vertex, axis of symmetry, xinter, yinter, domain, range

Algebra ->  Systems-of-equations -> SOLUTION: f(x)= -(x+3)(x+3)+3 Please help me find the vertex, axis of symmetry, xinter, yinter, domain, range      Log On


   

Question 351490: f(x)= -(x+3)(x+3)+3
Please help me find the vertex, axis of symmetry, xinter, yinter, domain, range
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The function is already in vertex form, y=a%28x-h%29%5E2%2Bk, where (h,k) is the vertex.
(h,k)=(-3,3)
The vertex lies on the axis of symmetry, x=-3
The parabola opens downward since a=-1%3C0 so the value at the vertex is the maximum.
There are no restrictions on the domain.
Domain:(-infinity,infinity)
Range:(-infinity,3)
To find the y-intercept, set x=0+ solve for y.
y=-%280%2B3%29%5E2%2B3=-9%2B3=-6
(0,-6)
.
.
To find the x-intercept, set y=0+ solve for x.
0=-%28x%2B3%29%5E2%2B3
%28x%2B3%29%5E2=3
x%2B3=0+%2B-+sqrt%283%29
x=-3+%2B-+sqrt%283%29
(-3%2Bsqrt%283%29,0)
(-3-sqrt%283%29,0)
.
.