Graphing Functions

1) The black graph is the function of y=x².

2)The orange graph is the function of y=x²+4. This is both a Transformation and a Vertical Translation of the function y=x². To perform this translation, add a number(in this case, 4) to the function. This will be the y-intercept.

3)The red graph is the function of y=(x-3)². This is both a transformation and a Horizontal translation of the function y=x². To perform this translation, place X in parentheses and add a negative number to translate it left or a positive number to translate it right(in this case, -3), then square the parentheses.

4)The green graph is the function of y=(x-3)²+4. This is a transformation, vertical, and horizontal translation of the function y=x². To perform this, combine both a vertical translation and a vertical translation by doing the processes of each on the same graph(in this case, putting X in (x-3) and squaring it for the horizontal translation and adding 4 for the vertical translation).

5)The brown graph is the function of y=(-x)². This is both a transformation and a horizontal Reflection of y=x² which reflects over the Y-Axis . To perform this, multiply x² with -1 and place it in parentheses and squaring it. Since y=x² is horizontally symmetrical, there is no change in the function when horizontally reflected.

6)The blue graph is the function of y= -x². This is both a transformation and a vertical reflection of y=x² which reflects over the X-Axis. To perform this, multiply x² with -1.

7)The purple graph is the function of y=-(x-3)²+4. This is a transformation, vertical translation, horizontal translation, and vertical reflection of the function y=x². To perform this, multiple steps are required. First, add 4 to X to make a vertical translation. Next, for the horizontal translation, place X in parentheses and add -3. Finally, for the vertical reflection, multiply the parentheses containing X with -1 and square it.