# Building Quadratic Functions to Describe Situations (Part 2)

ID: sufik-nabov
Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Standards: HSF-BF.A.1HSF-BF.A.1.aHSF-IF.C.7.aHSF-IF.B.5

14 questions

# Building Quadratic Functions to Describe Situations (Part 2)

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##### Sky Bound

A cannon is 10 feet off the ground. It launches a cannonball straight up with a velocity of 406 feet per second.

Imagine that there is no gravity and that the cannonball continues to travel upward with the same velocity.

Determine the height of the cannon ball, in feet above ground, at the given times.

1) ﻿$t$﻿ = 0 seconds

Show Work

2) ﻿$t$﻿ = 1 second

Show Work

3) ﻿$t$﻿ = 2 seconds

Show Work

4) ﻿$t$﻿ = 3 seconds

Show Work

5) ﻿$t$﻿ = 4 seconds

Show Work

6) ﻿$t$﻿ = 5 seconds

Show Work

7) ﻿$t$﻿ seconds

Show Work

8) Write an equation to model the distance in feet,﻿$d$﻿, of the ball ﻿$t$﻿ seconds after it was fired from the cannon if there was no gravity.

##### Tracking a Cannonball

Earlier, you found values that represented the height of a cannonball, in feet, as a function of time, in seconds, if there was no gravity.

9) This table shows the actual heights of the ball at different times

﻿$\begin{array}{|l|c|c|c|c|c|c|} \hline \\[-1em] \textbf{seconds} & 0 & 1 & 2 & 3 & 4 & 5 \\[-1em] \\ \hline \\[-1em] \textbf{distance} \\ \textbf{above ground} & 10 & 400 & 758 & 1,084 & 1,378 & 1,640 \\ \textbf{(feet)} \\[-1em] \\ \hline \end{array}$﻿

Compare the values in this table with those you found earlier. Make at least 2 observations.

10) Plot the two sets of data you have on the same coordinate plane.

11) How are the two graphs alike?

12) How are they different?

13) Write an equation to model the actual distance ﻿$d$﻿, in feet, of the ball ﻿$t$﻿ seconds after it was fired from the cannon. If you get stuck, consider the differences in distances and the effects of gravity from a previous lesson.

##### Graphing Another Cannonball

The function defined by ﻿$d=50+312t-16t^2$﻿ gives the height in feet of a cannonball ﻿$t$﻿ seconds after the ball leaves the cannon.

14) What do the terms ﻿$50$﻿, ﻿$312t$﻿, and ﻿$-16t^2$﻿ tell us about the cannonball?