1. Do Now from 1.1a… Solve algebraically and graphically…

2. More interesting info in Section 1.1 - grapher failure, hidden behavior, more problem solving…

3. First problem of the day… Find all x-intercepts of y = 3 2x – 5 Solving algebraically??? Solving graphically??? (there are no x-intercepts) This is an example of grapher failure – when a graphical model misrepresents the phenomena being studied

4. Try another problem: Solve graphically: x – 1.1x – 65.4x + 229.5 = 0 x = –9, 5, 5.1 This is an example of hidden behavior – when an inaccurate viewing window obscures details of a graph 32

5. Now, on to some basic problem solving… The engineers at an auto manufacturer pay students $0.08 per mile plus $25 per day to road test their new vehicles. 1. Derive an algebraic model for the students’ pay. p = 0.08x + 25 (where p = students’ pay, and x = miles driven)

6. Now, on to some basic problem solving… The engineers at an auto manufacturer pay students $0.08 per mile 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 3. John earned $93 test-driving a new car in one day. How far did he drive? 850 miles

7. 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 + 0.8 Total HW pts. Poss. HW pts. Total Q/T pts. Poss. Q/T pts.

8. 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% Grade =

9. 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 least 44.75 points

10. Now, on to some basic problem solving… At an air show, a pilot drops a smoke bomb to signal the start of the show. Ignoring air resistance, an object in free fall will fall d feet in t seconds, where d and t are related by: Approximately 3.354 sec 1. How long will it take the bomb to fall 180 feet?

11. Now, on to some basic problem solving… At an air show, a pilot drops a smoke bomb to signal the start of the show. Ignoring air resistance, an object in free fall will fall d feet in t seconds, where d and t are related by: Altitude: 2500 feet 2. 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?

12. Now, on to some basic problem solving… Solve the given equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. 1.2. Homework: p. 77-79 21, 23, 25-27 all, 39-47 odd