Question 24421
(1) {{{y = x^2 -4x -5}}}
convert to the form 
(2) {{{y = a(x - h)^2 + k}}}
I can factor the equation , but that doesn't help me. It factors to:
{{{(x - 5)(x + 1)}}}
I'll expand the form I'm trying to get it into
(3) {{{y = a(x^2 - 2 * h * x + h^2) + k}}}
Now I've got to make it fit equation (1)
(4) {{{y = a(x^2 -2*(2)*x + (2)^2) - 9}}}
That will make this form equal equation (1), but I have to make a = 1
equation (4) reduces to:
(5) {{{y = (x - 2)^2  - 9}}}
h = 2
k = -9
a = 1
what is the line of symmetry?
On the line of symmetry, +x gives me the same y as -x.

suppose the line of symmetry is x = 2, making y = -9
Now lets make x = (2 + j) or x = (2 - j)
(5) ends up looking like:
{{{y = (+j)^2 - 9}}}
or
{{{y = (-j)^2 - 9}}}
clearly the sign of j doesn't make a difference, so being on either side of
x = 2 gives the same y.
x = 2 is the axis of symmetry
I guess the answer to (c) is that you can look at the equation and tell what 
the important features are.
as for (d), put y = x into form (2), then
h = 0
k = 0
a = 1
The axis of symmetry is x = 0