Quadratic Equations - Square Root Property, Intro YouTube Video 4 81 8 Section 8.1 = or = = or = = or = Solve: 144 36 7 54 1
Quadratic Equations - Square Root Property YouTube Video Isolate the Square and then take the square root. 3 9 3t 6 0 3t 0 7 1 56 1 4 1 z 1
Completing the Square Warm Up: 1.. 3 4 4 4 6 9 3. 5 4. 10 5 1 1 1 1 6 144 1. Look at the previous and fill in the blanks without factoring: a) b) c) 4 4 8 16 6 9 d) 10 5 e) 1 3 9 f) 1 4 g) 8 h) 10 i) 5 So b 3
6 3 0 5 3 0 6 3 3 Try: 10 3 0 Try: 3 5 4
Non-Real comple solutions. Solve. = 144 = 1-3 = 48 (6 1) = 4 (4m 7) = 7 4 + 5 + 5 = 0 5
Quadratic Formula YouTube Video Section 8. a b c 0 b b 4ac a 3 4 0 Solve. k 6k 3 Solve. 0y 3y 0 6
DISCRIMINANT ----------- 0 0 One real solution b 4ac positive real negative imaginary 816 0 4 63 3 45 Find a number k such that the given equation has eactly one real solution. k 4 9 0 Determine if the equation can be solved using the zero-factor property or whether you can only use the quadratic formula? 5 + 70 + 49 = 0 + 4 + = 0 4 = 4 + 3 7
Equations Quadratic in Form. Section 8.3 OTHER PROBLEMS THAT INVOLVE QUADRATICS. 37 1) 4 16 ) 4 4/3 13 /3 + 9 = 0 3) ( 4) + ( 4) 0 = 0 5) 1 4 11 + = 0 6) 4 = 6 + 1 8
Formulas with Rational Equations YouTube Video Section 8.4 1 1 1, for c a b c ne I, for r R nr ( v1 v) t s, for t a c c for c 9
Applications of solving a + b + c = 0 YouTube Video 1) An envelope's length is 4 cm more than its width. The area is 96 cm. Find the length and the width. Define Length= Width= Equation 1: Equation : ) The base of a cardboard bo has a width that is 4 feet less than the length. The area is 117 ft. Find the length and the width. Define Length= Width= Equation 1: Equation : 3) An object is dropped from a height of 64 feet, how long will it take to hit the ground? It s position equation is s = 16t + 64 Hint: The ground has a height of 0, so s = 0 10
4) A rectangular piece of cardboard is in. longer than it is wide. A square piece 3 in. on a side is cut from each corner. The sides are then turned up to form an uncovered bo of volume 765 in 3. Find the dimensions of the original piece of cardboard. 5) Lyudmila wants to buy a rug for a room that is 0 ft long and 15 ft wide. She wants to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will she have if she buys a rug with an area of 34 ft? 11
Graphing Quadratics YouTube Video Warm up: Fill in the table below. Graph and label the ais of symmetry. f ( ) f ( 3 ) f () 3 9 f ( ) Section 8.5 What is happening to the graph of f ( ) in the following 1 f ( ) What is happening to the graph of f ( ) in the following? What is happening to the ais of symmetry? f ( ) ( 3) f ( ) ( ) f ( ) ( 1) What is happening to the graph of f ( ) f ( ) in the following? f ( ) 3 f ( ) 1 1
f ( ) a h k a= h= k= Verte= (h,k) ais of symmetry is =h Graph the following, label the verte, and ais of symmetry. f 5 f f 3 3 f f 3 f 1 f 1 f 3 f f 1 1 f f 3 1 13
Verte formula YouTube Video b, a P 3 P 6 y Section 8.6 Verte=(, ) Verte=(, ) P 1 3 P 3 1 1 Verte=(, ) Verte=(, ) 14
Verte formula - Applications b, a YouTube Video 1) Suppose the marketing department of Samsung has found that, when a certain model of cellular telephone is sold at a price of p dollars, the daily revenue R ( in dollars) as a function fo the price p is R(p) = 5p + 600p a) Define your variables y = = b) For what price will the daily revenue be maimized? c) What is the maimum daily revenue? ) Punkin Chunkin. Suppose that a catapult in the Punkin Chunkin contest releases a pumpkin 8 feet above ground at an angle with an initial speed. The model s(t) = 16t + 96t + 8 can be used to estimate the height s of the pumpkin after t seconds. a) Define your variables = = b) Determine the time at which the pumpkin is at a maimum height. c) determine the maimum height of the pumpkin. 15
3) FALLING OBJECT WITHOUT AIR RESISTANCE. h(t) = 16t + h 0 h 0 = the initial height, t = time in seconds, h(t) = height after t seconds A forest ranger drops a coffee cup off a fire watchtower. If the cup hits the ground 1.5 seconds later, how high is the tower? 4) A projectile is fired at an inclination of 45 to the horizontal. The height of the projectile is given by the function h, where is the horizontal distance from the firing point. 500 a) Find the maimum height of the projectile. b) How far from the firing point will the projectile strike the ground? c) When the height of the projectile is 100 feet above the ground, how far has it traveled horizontally? 16
Section 8.7 Solving Quadratic Inequalities YouTube Videos ( 7)( + 3) > 0 s 4s 1 0 3 5 9 < 5 17
4 + 4 > 0 Solving Quadratic Inequalities - Special Cases YouTube Videos 4 + 4 0 4 + 4 < 0 4 + 4 0 + 5 < 0 + 5 0 18
Rational inequalities YouTube Video 3 0 1 cannot = can equal= can equal cannot equal 5 0 cannot = can equal= 3 cannot = can equal= 19