Question 28694
[1]{{{y = x^2 -6*x + 8}}}
[2]{{{y = a*(x - h)^2 + k}}}
expand this
{{{y = a*(x^2 -2*h*x + h^2) + k}}}
Since the coefficient of x^2 is 1, make a = 1
group the constant terms together
{{{y = x^2 -2*h*x + (h^2 + k)}}}
{{{y = x^2 -2*h*x + (h^2 + k) = x^2 -6*x + 8}}}
Set the coefficients on the left equal to those on the right
-2h = -6
h = 3
h^2 + k = 8
9 + k = 8
k = -1
going back to [2]
{{{y = a*(x - h)^2 + k = (x - 3)^2 -1}}}
expand this to check
{{{(x - 3)^2 -1 = x^2 -6*x +9 -1}}}
OK
What is the axis of symmetry?
x = +3
check
does x + a give me the same y as x - a for any value of a?
plug in some values for x
y(3 + 1) = 0
y(3 - 1) = 0
y(3 + 2) = 3
y(3 - 2) = 3
a far out one
y(3 + 12) = 143
y(3 - 12) = 143
OK