Hi Brett C
This just a further comment to both avenues above, given that the Difference of Two Perfect Squares has no middle term the coefficient b is always zero. This is also the same for any binomial expressed in terms of x2 or y2 plus or minus any number just being shifted up or down by that constant in Standard Form. Keep in mind that in using the coefficients (-b/2a) you are viewing the following:
y = ax2 + 0x + c = ax2 + c
Instead of
y = ax2 + bx + c
There are other tests that can be run if you look into symmetry
If (x, y) exists on the graph, then the graph is symmetric about the:
X - Axis if (x, -y) exists on the graph
Y - Axis if (-x, y) exists on the graph
Origin if (-x, -y) exists on the graph
As for which test to run you can simply look at your given parabola
y = x2 - 9
Since this is y in terms of x, you would test for the Y axis first as follows:
Rewrite your parabola as
y = x2 - 32
Factor it as follows:
y = (x + 3)( x - 3)
Then make the recommended substitution to test for the y axis by substituting in -x for x
y = (-x + 3)(-x - 3)
Multiplying (and you can use FOIL if you are familiar with it) out gives
y =(-x)(-x) + 3x - 3x - 9
y = x2 - 9
You should test this for similar problems like:
y = x2 - 5, the axis of symmetry is the y axis or x = 0
x = y2 - 7, the axis of symmetry is the x axis or y = 0
Finally, you can review the relationship between the vertex of a parabola and its line of symmetry. The axis of symmetry passes through the vertex of the plot whether it opens up or down or right or left.
I hope you find the info above useful and keep in mind that a test question might not be just the difference between two perfect squares and you could be given a horizontal parabola. You can typically graph your quadratic to see the vertex as a check.
