SOLUTION: Graph and give the coordinates of the vertex,x and y intercepts, and graph {{{y=f(x)=-x^2-6x}}}

Algebra ->  Linear-equations -> SOLUTION: Graph and give the coordinates of the vertex,x and y intercepts, and graph {{{y=f(x)=-x^2-6x}}}      Log On


   

Question 172128: Graph and give the coordinates of the vertex,x and y intercepts, and graph
y=f%28x%29=-x%5E2-6x
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the vertex (h,k), the easiest way is to use the formula
h=-b%2F%282a%29
So here, a=-1, b=-6, and c=0, so
h=-%28-6%29%2F%282%28-1%29%29=6%2F%28-2%29=-3
To find k, you just evaluate the function at x=-3. So
f%28-3%29=-%28%28-3%29%5E2%29-6%28-3%29=-9%2B18=9
So the vertex is (-3,9). The y intercept is found by setting x equal to 0.
f%280%29=-0%5E2-6%280%29=0
So the y intercept is the origin, (0,0).
The x intercepts are found by setting y = 0.
0=-x%5E2-6x
Factoring, we get
0=x%28-x-6%29
So
x=0 and -x-6=0
So our two x intercepts are at x=0 and x=-6.
Finally, graphing, we get
graph%28300%2C200%2C+-10%2C10%2C-10%2C10%2C-x%5E2-6x%29