Question

Graph the equation y=-x^2+12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answer 1

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.