Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 1 Do Now: Solve for x: Using interval notation: Solution: or WHEN MULTIPLYING OR DIVIDING BY A NEGATIVE, REMEMBER TO REVERSE THE INEQUALITY SIGN!!! Parenthesis does not include the endpoint. Bracket includes the endpoint. Infinity never gets a bracket.

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 2 Solve for x and show your answer in interval notation and on a number line:

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 3 Consider two cases: II. Quadratic < 0I. Quadratic > 0 Solving Quadratic Inequalities algebraically: HW p. A73 # 55,56

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 4 Solve the Quadratic Inequality algebraically: HW p. A73 # 55,56

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 5 Solving Quadratic Inequality graphically: Since we want the inequality to work for all values of that are below 7, we want all the values between the left and right POI’s (See shaded region). Thus the solution is: HW p. A73 # 55,56

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 6 Quadratic Inequality Application: A projectile is fired straight upward from ground level with an initial velocity of 384 feet per second. During what time period will its height exceed 2000 feet? The position of an object moving vertically can be modeled by the position equation: s is the height and t is the time. In this case s 0 = 0, v 0 = 384, and s must be greater than 2000 so: HW p. A74 #81, 83

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 7 You must adjust the Zoom and Window settings to get a clear picture of the intersection of the 2 graphs. Try Zoom Fit and change the Window settings as indicated in the image: HW p. A74 #81, 83

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 8 HW p. A74 #81, 83 SOLUTIONS TO HOMEWORK PROBLEMS (Quad Ineq. Apps) #81: A projectile is fired straight upward from ground level with an initial velocity of 160 feet per second. (a)At what instant will it be back at ground level? (b)When will the height exceed 384 feet? (a) (b) When the projectile is at ground level the height, s, is zero. We are finding t when s = 0. Range of t values when the height of the projectile is above 384

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 9 SOLUTIONS TO HOMEWORK PROBLEMS (Quad Ineq. Apps) #83: The numbers D of doctorate degrees (in thousands) awarded to female students from 1990 to 2003 in the US can be approximated by the following model, where t is the year, with t = 0 corresponding to 1990: HW p. A74 #81, 83 (a) Use a graphing utility to graph the model

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 10 (b) Use the zoom and trace features to find when the number of degrees was between 15 and 20 thousand. The blue line indicates the interval where the curve is between the 15 and 20

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 11 (d) According to the model, will the number of degrees exceed 30 thousand? If so, when? If not, explain. (c) Algebraically verify your results from part (b) Show using a number line why the solution is:

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 12 Use the models which approximate the annual numbers of hours per person spent reading daily newspapers N and playing video games V for the years 2000 to 2005, where t is the year, with t = 0 corresponding to 2000.

Aim: HOW DO WE SOLVE INEQUALITIES?HW: p.A73 #11-24 even 13 Review the 4 situations when dealing with conjunctions and disjunctions: