Question

figure 1
figure 2
figure 3
$y = 0.28x^{2}+1.87x$
$y = 1.5x^{2}-125.3x + 2675$
$y = 0.12x^{2}+1.1x + 104.4$
(a) which curve fits the data best?
$circ$ figure 1 $circ$ figure 2 $circ$ figure 3
(b) use the equation of the best fitting curve from part (a) to predict the
distance required to stop the train when it is travelling 40 kilometers per
hour. give an exact answer, not a rounded approximation.
$square$ meters

Explanation:

Step1: Evaluate curve fit accuracy

Visually compare data points to each curve: Figure 1's points lie closest to its regression line, with minimal deviation, so it is the best fit.

Step2: Substitute x=40 into Figure1's equation

Use $y=0.28x^2 + 1.87x$, replace $x$ with 40.
First calculate $0.28(40)^2$:
$0.28\times1600 = 448$
Then calculate $1.87\times40 = 74.8$

Step3: Sum the two results

Add the two values to find $y$.
$448 + 74.8 = 522.8$

Answer:

(a) Figure 1
(b) 522.8 meters