Find the axis of symmetry for y = -x^2 + 6x -9?

Answer 1

Given:
y = -x² + 6x -9
To find axis of symmetry.
y = -x² + 6x -9
dy/dx = -2x + 6 (equation for slope).
-2x + 6 = 0
-2x = -6
x = -6 /-2
x = 3
The axis of symmetry is the x = 3 axis.

When the slope equals zero, it will contain the axis symmetry point.

Answer 2

the form of the equation is a parabola with axis parallel to the y axis. so the axis goes through the minimum. differentiate y' = -2x+6, solve for 0 to get x=3. so the axis is the line x=3. to check, see what y is on two places the same distance away, say x=0 and x=6

if x=0 , y = 0^2+ 6*0 -9 = -9
if x = 6 y = -6^2 + 6*6 -9 = -9

looks good

Answer 3

Use the formula x = -b/2a.
Here a=-1 (the coefficient in front of x^2)
b=6 (the coefficient in front of x)
Therefore, we have
x = -6/((2)(-1)) = -6/-2 = 3
x = 3 is the equation of the axis of symmetry.

Answer 4

y = -x^2 + 6x - 9

x = (-b)/(2a)

x = (-6)/(2(-1))
x = -6/(-2)
x = 3

y = -(3)^2 + 6(3) - 9
y = -(9) + 18 - 9
y = -9 + 18 - 9
y = 9 - 9
y = 0

ANS : (3,0)