Algebra 1 Word Problem

Question

A superhero leaps from a building to capture a villian. The data from his leap is shown below. 

Time(seconds): .75|1.5|2|2.25|2.75|3.5

Height(feet): 108|119|116|112|97|59

 

This is a quadratic function.

 

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

 

2) Determine the initial velocity of the superhero's jump and the height of the building. Round to the nearest hundredth.

 

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

 

Please do all problems, and show work!! Thank you! 

Answer 1

1)

 

On your graphing calculator, go to STATS, then EDIT.  You should see a 3-column table.  Make sure you clear all values before entering the values from this specific problem.  In the first column, label all the time values in the order given.  In the second column, label all the height values that correspond to the time values.  Then once you have recorded your values, go the STATS, CALC, and scroll down to select QUADRegression.   It will give you the equation based on the values you gave on the chart.

 

Write your equation in the form

 

h = at² + bt + c

 

where:

t = time (seconds)

h = height (feet)

 

Note: the value of "a" should be negative, since the height values increase then decrease.

 

 

2)

 

The initial velocity is the value of b

The height of the building is the value of c.  Or you can evaluate h at t=0.

 

 

3)

 

Set h=0 and solve for t.  Choose the positive value of t.