Question

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. (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 50 kilometers per hour. give an exact answer, not a rounded approximation. meters

Explanation:

Step1: Visual inspection for best - fit

Visually, the curve in Figure 2 appears to pass closer to most of the data points compared to the other two curves. So, the best - fitting curve is from Figure 2.

Step2: Substitute value into the equation

The equation of the curve from Figure 2 is $y = 0.28x^{2}+2.25x$. We are given that $x = 50$ (speed in km/h). Substitute $x = 50$ into the equation:
\[

$$\begin{align*} y&=0.28\times(50)^{2}+2.25\times50\\ &=0.28\times2500 + 112.5\\ &=700+112.5\\ &=812.5 \end{align*}$$

\]

Answer:

(a) Figure 2
(b) $812.5$