Question

make a scatterplot of the data and graph the function on the same coordinate grid. calculate the residuals and make a residual plot. describe the fit of the function to the data. \\( f(x)=3x^2 - x + 1 \\)\

x	y	\
-2	18	\
-1	10	\
0	5	\
1	3	\
2	11	\

\
make a scatterplot of the data and graph the function on the same coordinate grid. choose the correct answer below.\
\\( \circ \\) a\
\\( \circ \\) b\
\\( \circ \\) c\
\\( \circ \\) d

Explanation:

Step1: Calculate predicted y-values

For each $x$, compute $f(x)=3x^2 - x + 1$:

• $x=-2$: $3(-2)^2 - (-2) + 1=3(4)+2+1=15$
• $x=-1$: $3(-1)^2 - (-1) + 1=3+1+1=5$
• $x=0$: $3(0)^2 - 0 + 1=1$
• $x=1$: $3(1)^2 - 1 + 1=3-1+1=3$
• $x=2$: $3(2)^2 - 2 + 1=12-2+1=11$

Step2: Match data points to plot

Original data points: $(-2,18), (-1,10), (0,6), (1,17), (2,17)$. The function $f(x)$ is a upward-opening parabola. Option B shows the parabola passing near the calculated predicted points, with the original data points plotted correctly relative to the curve.

Step3: Confirm correct plot

Compare all options: only Option B aligns both the parabola shape of $f(x)$ and the positions of the given data points.

Answer:

B