Answer
Vertex: (3,0)
X-intercept: (3,0)
Y-intercept: (0,-9)
Work Step by Step
To find the vertex of the formula, you must find your A, B, and C values. For this equation, A= -1, B=6, and C= -9.
To find the x value, let x= -B/2A. so...
x= -6/2(-1)
x= -6/-2
x= 3
Now plug the x just found into the equation.
-(3)^2+6(3)-9= f(x)
-9+18-9= f(x)
9-9=f(x)
0=f(x)
so (3,0) is the vertex.
To find the x intercept, plug 0 into the y value.
0= -x^2+6x-9
Factor the equation. Find two values that will add to give you the B value, and multiply to give you the C value.
For this equation, -(x-3)^2
set (x-3)=0
add 3 to both sides, and x=3.
so the x-intercept is (3,0)
To find the y intercept, plug in 0 to all of the x values.
f(x)= -0^2+6(0)-9
f(x)= 0+0-9
f(x)= -9
So the y-intercept is (0,-9)
To graph the equation, i'm going to plug in 2 and 4 for the x values.
y=-(2)^2+6(2)-9
y=-4+12-9
y=8-9
y=-1
so one point would be (2,-1)
y=-(4)^2+6(4)-9
y=-16+24-9
y=8-9
y=-1
So another point would be (4,-1)
