©2018TheAlgebros,LLC

2.4GraphingPolynomialFunctions

Use a graphing utility to find the extrema for each of the following functions. If necessary, round to the nearest hundredth.

1. !(#) = 3#* − #, − 12# + 8 2. 8(#) = 60#* − 187#, + 188# − 60

3. 9(#) = −2#* + 11#, + 4.35# − 0.9 4. !(#) = 3#( − 9#* − 117#, + 141# + 630

Use your calculator to find the zeros, find the extrema and tell the end behavior. If necessary, round to the nearest hundredth.

5. !(#) = 4#* − 3#, − 2# + 1 6. :(#) = 4#* − 240#, − 6400# 7. !(#) = − ;;<<

#* + *;<#, + 40#

Solve the following equations by factoring:

8. #( − 14#, = −45 9. −2#* + 16#, − 32# = 0

4. The volume of air in the human lungs measured in liters can be described by the following function:

=(>) = −0.035>* + 0.152>, + 0.173>, where t is time in seconds.

a. Estimate the zeros using your calculator.

b. Based on the graph in your calculator, how long do you think a respiratory cycle lasts?

c. How long does it take to maximize the volume of air in a human’s lungs?

2.4 PRACTICE

RELATIVEMAXOF 16.03 AT XI I 05 ABSOLUTEMINOF 6.25ATX 0.87 AND X I 2.87RELATIVE MINOF 2.71 AT XI 1.27 RELATIVEMAX OF 6 AT X

ABSOLUTEMINRELATIVEMAX OF 64.72AT XI 3.85 RELATIVEMAXOF 671.01 AT XI 0.57 Of 886.9RELATIVEMinor I 32 AT XT O 19 RELATIVE MIN OF 476.23 AT XI 3,76 AT 5,4

MAXOF 1.25 AT XI 023 RELATIVEMaxor 36,110AT XI 10.55 RelativeMaxor 1505.30AT 21 4786MIN OF 0 50 AT XI 0.73 RELATIVE MIN 420110AT Xp so 55 RELATIVEMIN 665.30AT XI 27.86ZEROS 21 1 XI 0.64 zeros X 20 ZEROS X 50

X 20.39o X O

X 80 X 80END BEHAVIOR END BEHAVIOR END BEHAVIORX no Fox x

X no Fox x X no Fox xx x Fox x

X x Fox x X D Fox x

2 1 2 8 116 OT 2 1 412 0

x 9112253 0 fx 311316511 53 0 Lx 3 x 5 X O X 4

X Z O 94 21 0 X I 5,28

ABOUT 5.28 Sec

RELATIVE MAX AT X 23.38ABOUT 3,38 SECONDS IS WHENOUR LUNGS ARE FULL