Question

which transformation of the graph of y=x^2 would result in the graph of y=x^2+2

Answer 1

Is this a multiple choice question?

Answer 2

yeah here are the answers:
a) r(y-2)
b) T(0,2)
c) R(0,90degrees)
d) Dilation 2

Answer 3

\(\large {
\textit{function transformations}
\\ \quad \\

\begin{array}{llll}

\begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\cdot {\color{blue}{ B}}\end{array}
\qquad
\begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array}

\begin{array}{llll}{\color{green}{ D}} > 0& Up\\ {\color{green}{ D}} < 0 & Down\end{array}
\\

\qquad \downarrow\qquad\qquad\qquad \downarrow\\
y = {\color{purple}{ A}} ( {\color{blue}{ B}}x + {\color{red}{ C}} ) + {\color{green}{ D}}\\
\qquad\qquad\uparrow \\

\qquad\begin{array}{llll} horizontal\\ shift\\ by \ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\end{array}

\begin{array}{llll}\frac{{\color{red}{ C}}}{{\color{blue}{ B}}} > 0 & to \ left\\ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}} < 0& to \ right\end{array}
\end{array}
}\)

what do yiou think?

Answer 4

A rotation would not move the line 2 spaces up. A dilation would extend the slope of the line, not move it up. A reflection over y=2 would cause the slope to be negative. So, what answer are you left with?

Answer 5

oops dont wanna ruin his choice :D

Answer 6

that makes sense, thank u @BunnyBree !!

Answer 7

not really what this means @jdoe0001 but thanks anyway!

Answer 8

You're very welcome! (: