[tex]x^{2}[/tex]Answer:
(Explanation)
Step-by-step explanation:
Part A:
The graph of y = [tex]x^{2}[/tex] + 2 will be translated 2 units up from the graph of y = [tex]x^{2}[/tex].
If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the [tex]x^{2}[/tex], which is why it doesn't translate left.
This is what graph A should look like:
[Attached File]
Part B:
The graph of y = [tex]x^{2}[/tex] - 2 will be translated 2 units down from the graph of y = [tex]x^{2}[/tex].
If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the [tex]x^{2}[/tex], which is why it doesn't translate right.
This is what graph B should look like:
[Attached File]
Part C:
The graph of y = 2[tex]x^{2}[/tex] is a stretched version of the graph y = [tex]x^{2}[/tex]. Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.
This is what graph C should look like:
[Attached File]
Part D:
The graph of y = [tex]\frac{1}{2}x^{2}[/tex] is a compressed version of the graph y = [tex]x^{2}[/tex]. Numbers that are in-between 0 and 1, and -1 and 0 are compressed.
This is what graph D should look like:
[Attached File]
