Our project for chapter P is graphing parent functions. In this project, we had to make some transformations to the parent functions. The transformations were Horizontal & Vertical Translations, and also Reflections across the X-axis and Y-axis. The parent function that I graphed was the Quadratic Function y= x^2 (Top left corner graph).
First, I graphed the original function (y=x^2) in black.
Then, I did a Horizontal Translation 4 units to the right in red which has the equation (y=(x-4)^2).
Next I did a Vertical Translation 5 units up in blue which has the equation (y=x^2 +5).
After that, I did a combination of both a Horizontal and Vertical Translation which makes the original graph shifts right by 4 units and up by 5 which is represented by the equation (y=(x-4)^2 + 5) in purple.
Now we go on with the reflections.
First, i did a Reflection across the Y-axis, it basically just flipped the original graph around across the Y-axis in green(on top of original graph in black) which look exactly like the original graph and gives us the equation (y=(-x)^2).
Then I did a Reflection across the X-axis which flips the original graph across the X-axis like the one in pink which is represented by the equation (y=-x^2). Last but not least.
I combined all the transformation made in this graph.
I did a Vertical and Horizontal Translation of 5 units up and 4 units right followed by a Reflection across the X-axis in orange which gives me the equation (y=-(x-4)^2 -5).