Axis of Symmetry of the Quadratic Formula

Yesterday we learned about the Quadratic Formula, which lets us turn ax²+bx+c=0, into: x=(-b÷2a)+/-(√b²-4ac)÷2a. We learned how to take the roots(where the line crosses the x axis) from that equation.

Now today, we learned how to take the Axis of Symmetry(the line which seperates the graph to create a mirror image) from that equation also.

The Axis of Symmetry (AoS from now on) is taken from the equation directly.

x=(-b÷2a)+/-(√b²-4ac)÷2a

The AoS would be (-b÷2a) and yes, it's as simple as that. :)

For example:

Find the roots and the AoS of 4x²-6x-2=0 using the quadratic formula.

It's typically a good idea to write a=_, b=_, c=_, so you could have it for reference.

a=4, b=-6, and c=-2

1)x=(-b÷2a) +/- (√b²-4ac)÷2a --Starting Equation

2)x=(-(-6)÷2(4))+/-(√(-6)²-4(4)(-2))÷2(4) --Substitute in the numbers

3)x= (6÷8)+/-(√36+32)÷8 --Simplify

4)x=(6÷8)+/-(√68)÷8 --Combine like terms

5)x=(6÷8)+/-(2√17)÷8 --Simplify the term under the root sign, if possible.(68÷4=17, 8÷4=2)

AoS= x=6÷8=3÷4

Root#1:x=(6÷8)+(√17)÷4 Divide the denominator (8) by the coefficient (2)
and;
Root#2:x=(6÷8)-(√17)÷4

Feel free to ask any questions/comment if needed, and the next person to blog is Lisaaaa. :)