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.
$f(x)=2x^2 - 2x + 1$

$x$	$y$

make a residual plot. choose the correct answer below.
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

help me solve this view an example get more help .

Explanation:

Step1: Calculate predicted y-value

First, substitute $x=-2$ into $f(x)=2x^2-2x+1$:
$$f(-2)=2(-2)^2-2(-2)+1=2(4)+4+1=8+4+1=13$$

Step2: Compute residual

Residual = Observed $y$ - Predicted $y$
$$\text{Residual}=8-13=-5$$

Step3: Match residual plot

The residual for $x=-2$ is -5, which corresponds to the point $(-2, -5)$. This point is only present in plot B, so it is the correct residual plot.

Answer:

B