~*♥*~ Symmetry on the axis ~*♥*~
The axis of symmetry is nothing but a line that passes through the vertex of the parabola on the graph and it's like a mirror. With this being the case, we will use this to graph the other half of the parabola. The book definition, however, says this, and I directly quote...
"axis of symmetry of a parabola : The line perpendicular to the parabola's directrix and passing through its focus..."
Does that sound a bit odd to you?
But anyway, when it's plotted ON a graph, it should look a little something like this:
But first, of course, you have to have the vertex in order to find it's axis of symmetry. Now, being as though this section isn't all that long, it won't be that much to squint at. Let's check out a few examples here, shall we?
Ex.
y = x² − 4x + 5x = -b ÷ 2a This is the formula for standard equations
x = -(-4) ÷ 2 (1)
x = 1
Axis of symmetry x = 1
Easy enough? Let's do two more.
Ex.
y = x² - 6x + 5
x = -b ÷ 2a
x = -(-6) ÷ 2(1)
x = 3
Axis of symmetry x = 3
Ex.
y = x² + 8x + 15
x = -b ÷ 2a
x = -8 ÷ 2(1)
x = -4
Axis of symmetry x = -4
So, latched on yet? If so, good for you! You're ready for the test! Just kidding. But if not, here are some practice problems for you.
~*♥*~Test your strength ~*♥*~
1. y = x² - 2x - 3
2. y = x² - 4x + 10
3. y = x² - 10 + 17
4. y = x² + 16 - 2
5. y = x² + 12 - 11
