Question

figure 1
figure 2
figure 3
(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 speed
of the object at 7 seconds. give an exact answer, not a rounded
approximation.
□ meters per second

Explanation:

Part (a)

Step1: Analyze Figure 1

The equation for Figure 1 is a downward - opening parabola ($y = - 0.2x^{2}+21.2x - 7.7$) with a negative leading coefficient. But the data points seem to have a trend that is more consistent with an upward - opening parabola as $x$ increases, so Figure 1 is not a good fit.

Step2: Analyze Figure 2

The equation for Figure 2 is $y=0.7x^{2}+0.8x + 13$ (upward - opening parabola). Visually, the curve in Figure 2 passes close to most of the data points. The data points seem to follow the increasing and accelerating trend of the quadratic curve in Figure 2.

Step3: Analyze Figure 3

The equation for Figure 3 is $y = 0.5x^{2}-4.9x + 60.4$. The vertex of this parabola is at $x=-\frac{b}{2a}=-\frac{- 4.9}{2\times0.5}=4.9$. The data points do not seem to follow the "U - shaped" trend (with a minimum around $x = 5$) as well as Figure 2 follows its data points.

Step1: Identify the equation

From part (a), the best - fitting curve has the equation $y = 0.7x^{2}+0.8x + 13$.

Step2: Substitute $x = 7$

We substitute $x = 7$ into the equation:

$$
LATEXBLOCK0
$$

Answer:

Figure 2

Part (b)