Answer:
To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.
The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).
To find the roots, we need to set y=0 and solve for x:
0=-x^2+12x-35
x^2-12x+35=0
(x-5)(x-7)=0
x=5 or x=7
So the roots are (5,0) and (7,0).
The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.