This project was based on the parent** functions** in Chapter P. We had to make transformations from the parent functions. The **transformations** we had to create were **vertical translations, horizontal translations,** and **reflections **across the **x-axis** and** y-axis**. The parent function that I will explain about is the squaring function, x^{2}.

The original function x^{2 }is in blue.

The vertical translation, function of y= x^{2 }+2, is shown in orange. It was a vertical shift up 2 units.

The horizontal translation, function of y= (x-2)^{ 2}, is shown in magenta. It was a horizontal shift right 2 unit.

The vertical and horizontal translation, function of y= (x-2)^{ 2 }+1, shown in red. It was a horizontal shift right 2 unit, vertical shift up 1 unit.

The horizontal reflection, function of y= -x^{2}, shown in pink. I flipped the parent function graph across the x-axis.

The vertical reflection, function of y= -x^{2} -1, shown in green. It was a reflection and vertical shift down 1.

The vertical shrink and stretch, function of -2x(x+1)^{ 2 }-3, shown in purple. It was a reflection, horizontal shift left 1, and vertical shift down 5 and vertical stretch by 2.

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