Question

use your notes from todays lesson (wed. feb. 11) to help you complete and submit this assignment.assignment is due wednesday feb. 11th by the end of the day.multiple choice 12.5 points16. the graph of $f(x) = x^2$ was transformed to create the graph of $h(x) = 3f(x)$. which graph represents quadratic functions $f$ and $h$?abcdabcdclear my selection

Explanation:

Step1: Identify base function points

For $f(x)=x^2$, key points:
When $x=0$, $f(0)=0^2=0$;
When $x=1$, $f(1)=1^2=1$;
When $x=2$, $f(2)=2^2=4$.

Step2: Calculate transformed function points

For $h(x)=3f(x)=3x^2$, key points:
When $x=0$, $h(0)=3(0)^2=0$;
When $x=1$, $h(1)=3(1)^2=3$;
When $x=2$, $h(2)=3(2)^2=12$.
This is a vertical stretch of $f(x)$ by a factor of 3, so each y-value of $f(x)$ is multiplied by 3, keeping the vertex at (0,0) and narrowing the parabola.

Step3: Match to correct graph

Compare the points to the options: Option C shows the original parabola $f(x)=x^2$ and a narrower parabola passing through (1,3), (2,12), which matches $h(x)=3f(x)$.

Answer:

C. <The graph labeled C with the original $f(x)=x^2$ parabola and a vertically stretched parabola $h(x)=3x^2$>