A super hero leaps from a building to capture a villain. The data from this leap is shown below

Question

Time(seconds) .75 | 1.5 | 2 | 2.25 | 2.75 | 3.5
Height(feet) 108 | 119 | 116| 112 | 97 | 59


1. What type of function best models this data
linear exponential quadratic or other

2. Use a graphing calculator to perform a regression for the best fit equation. Write the resulting equation below, rounding to the nearest hundredth.

3. Calculate how many seconds it takes for the super hero to land on the ground (assume no flying powers used) show your work and round to the nearest hundredth

Answer 1

Time(seconds) .75 | 1.5 | 2 | 2.25 | 2.75 | 3.5
Height(feet) 108 | 119 | 116| 112 | 97 | 59


1. What type of function best models this data
linear exponential quadratic or other: It may be a parabola ( Quadratic)

2. Use a graphing calculator to perform a regression for the best fit equation. Write the resulting equation below, rounding to the nearest hundredth.

The obtained equation for the trend line is

Y = -16.27 X² +51.45 X + 78.58 , this gives a R²= 0.9999 which is almost perfect.

 

3. Calculate how many seconds it takes for the super hero to land on the ground (assume no flying powers used) show your work and round to the nearest hundredth

 

making the equation equal to zero you will obtain the time. X, take into account that when time is zero, the height is 78 feet. Search for the logic time.