4-3

Chapter four is about a lot of different things. The test on these things is Tuesday. Great. Anyway this week my blog will be on symmetry.
To check for symmetry:

1. About the x-axis
a. Put a negative in front of y and simplify. The new equation is symm. About the x-axis.
b. If it matches the original it is symmetric about the x-axis.

2. About the y-axis
a. Plug in a (-x). The new equation is symm. About the y-axis.
b. If it matches the original it is symmetric about the y-axis.

3. About the origin
a. Plug in a (-x) and put a negative in front of y. The new equation is symm. about the origin.
b. If it matches the original it is symmetric about the origin.

4. About y=x
a. Switch the x and y and solve for y. The new equation is symm. about y=x.
b. If it matches the original it is symmetric about y=x

EXAMPLE
Is y=x^2+9 symmetric about I) the x-axis, II) the y-axis, III) the origin, IV) y=x

I. –y=x^2+9 In this equation you can reverse the signs.
Y=-x^2-9 Since the equations do not match, it is not symm about the x axis.

II. y=(-x)^2+9 Since the negative is inside (), it will stay negative.
y= -x^2+9 The equations do not match therefore it is not symm about the y axis.

III. -y= (-x)^2+9 Reverse the signs.
y= x^2-9 Not sym about origin.

IV. x=y^2+9 Since it is impossible to change this back to x^2, you automatically know that it is not symmetric about y=x.

Good luck guys. Oh and since B-Rob is in California does that mean this has to be posted by midnight her time or our time? o_O

--Sarah