Do Now from 1.1a…

Solve algebraically and graphically…

211 121x

2 23 4 2 7 8x x x x

22,0x

2,6x

More interesting info in More interesting info in Section 1.1 - grapher Section 1.1 - grapher

failure, hidden behavior, failure, hidden behavior, more problem solving…more problem solving…

First problem of the day…

Find all x-intercepts of y =3

2x – 5

Solving algebraically???Solving algebraically???

Solving graphically??? Solving graphically??? (there are no x-intercepts)

This is an example of This is an example of grapher failuregrapher failure – when a – when agraphical model misrepresents the phenomenagraphical model misrepresents the phenomenabeing studiedbeing studied

Try another problem:

Solve graphically: x – 1.1x – 65.4x + 229.5 = 0

x = –9, 5, 5.1x = –9, 5, 5.1

This is an example of This is an example of hidden behaviorhidden behavior – when – whenan inaccurate viewing window obscures detailsan inaccurate viewing window obscures detailsof a graphof a graph

3 2

Now, on to some basic problem solving…

The engineers at an auto manufacturer pay students $0.08 permile plus $25 per day to road test their new vehicles.

1. Derive an algebraic model for the students’ pay.

p = 0.08x + 25p = 0.08x + 25

(where p = students’ pay,(where p = students’ pay,and x = miles driven)and x = miles driven)

Now, on to some basic problem solving…

The engineers at an auto manufacturer pay students $0.08 permile plus $25 per day to road test their new vehicles.

2. How much did the auto manufacturer pay Sally to drive 440 miles in one day? $60.20$60.20

3. John earned $93 test-driving a new car in one day. How far did he drive? 850 miles850 miles

Now, on to some basic problem solving…

A math student’s grade is determined by weights, with home-work counting 20% and quizzes/tests counting 80%.

1. Derive an algebraic model for the student’s grade, given that homework and quizzes/tests are graded by points.

g = 0.2 + 0.8g = 0.2 + 0.8Total HW pts.Total HW pts.

Poss. HW pts.Poss. HW pts.

Total Q/T pts.Total Q/T pts.

Poss. Q/T pts.Poss. Q/T pts.

Now, on to some basic problem solving…

A math student’s grade is determined by weights, with home-work counting 20% and quizzes/tests counting 80%.

2. What is Wolfgang’s grade if he has earned 26 out of a possible 28 homework points, quiz grades of 22/25 and 13/15, and a test grade of 41/50?

86.127%86.127%

Grade = 26 22 13 410.2 0.8

28 25 15 50

Now, on to some basic problem solving…

A math student’s grade is determined by weights, with home-work counting 20% and quizzes/tests counting 80%.

3. If Jan has perfect homework scores and quiz scores of 20/25 and 14/15, what does she need to earn on the upcoming

50-point test in order to have an overall 90% grade average?

At leastAt least44.75 points44.75 points

20 140.2 1 0.8 0.9

25 15 50

x

Now, on to some basic problem solving…

At an air show, a pilot drops a smoke bomb to signal the startof the show. Ignoring air resistance, an object in free fall willfall d feet in t seconds, where d and t are related by:

Approximately 3.354 secApproximately 3.354 sec

216d t1. How long will it take the bomb to fall 180 feet?

216 180t

Now, on to some basic problem solving…

At an air show, a pilot drops a smoke bomb to signal the startof the show. Ignoring air resistance, an object in free fall willfall d feet in t seconds, where d and t are related by:

Altitude: 2500 feetAltitude: 2500 feet

216d t2. If the bomb is in free fall for 12.5 seconds after it is dropped, how high was the airplane when the bomb was dropped?

Now, on to some basic problem solving…

Solve the given equation graphically by converting it to anequivalent equation with 0 on the right-hand side and thenfinding the x-intercepts.

3 2 2 8x x 1.

1.086,2.864x

35 2x x x 2.

1.758x

Homework: p. 77-79 21, 23, 25-27 all, 39-47 odd