Question

the data points show the distance ( y ) (in meters) required to stop a train traveling at a speed ( x ) (in kilometers per hour). each figure has the same data points. however, each figure has a different curve fitting the data. the equation for each curve is also shown. answer the questions that follow.
figure 1
( y = 0.28x^2 + 18.7x )
figure 2
( y = -0.12x^2 + 25.1x - 52.1 )
figure 3
( y = 21.3x + 105.5 )
(a) which curve fits the data best?
figure 1
figure 2
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.
meters

Explanation:

Step1: Identify best fitting curve

Observe that Figure 1's curve passes closest to all data points, matching the trend of the data better than the other curves.

Step2: Substitute x=40 into Figure1's equation

Use $y=0.28x^2 + 1.87x$, substitute $x=40$.
First calculate $x^2$: $40^2=1600$
Then compute each term:
$0.28\times1600 = 448$
$1.87\times40 = 74.8$
Sum the terms: $448 + 74.8 = 522.8$

Answer:

(a) Figure 1
(b) 522.8 meters