Welcome Back from March Break! (Easter break in 2 weeks + 4 days if you care)

Transcription

1 Welcome Back from March Break! (Easter break in 2 weeks + 4 days if you care) Events for the Week: Mon: Lesson 2.8 Solving Quadratic Equations: Word Problems (pretty much the same as Gr. 10) Please show me hmwk during today's hmwk time if incomplete before March Break Tues: No math class (meet here in Room 232 assembly in cafeteria: about 10 classes are going) Funny Money Assembly Wed: Last Lesson of Unit 2.9 Linear and Quadratic Systems Thurs: Review Parent Teacher Night: 6 pm 8 pm (if you gave me your personal ; I need to re input) Friday: UNIT 2 TEST: Quadratic Functions & Equations (pink sheet outline) 1

2 Quiz Take up Show five key points (you should not need a table of values) You should be able to simply use the vertex (3, 4) and the step values: (1, 4, 9, 16, 25, 36) but a = 2 so step values are 2, 8, 18, 32, 50, y intercept: (did not lose marks but should be able to do this with ease) Method I: When x=0, what is the value of y y vertex (3, 4) zeros x = 2(9) +4 = 18+4 = 14 Method II: Step Value When 3 left of vertex, the y step value will be 2 times 3 2 = 18 (b/c a = 2) so... down 18 from 4 = 14 zeros: (did not lose marks for not finding value but should be able to do this with ease) 5 6 x=3 KEY CONCEPT: Zeros occur on the x axis where y=0 Set y=0 and find the value of x (typically two values) unless parabola i) doesn't cross x axis or ii) parabola just touches x axis in one spot or 2

3 Complete the square in order to find and state the maximum or minimum value of and the value of x when it occurs. a is negative so parabola opens down such that there is a maximum Exact wording from homework. Step 1: Factor coefficient from FIRST TWO TERMS (note: sign change!) ` Step 2: Find the special # and ADD IT and SUBTRACT IT (divide 8 by 2 then square it) Step 3: Write as perfect square trinomial (note the number is half of the factored 'b') Step 4: Clean up to express in vertex form Step 5: The vertex is (4, 49). A maximum value of 49 occurs when x=4. State the max/min value and the value of x when it occurs. 3

4 2.8 Solving Quadratic Equations: Word Problems I. Measurement (unlimited possibilities: dining room p127, hmwk #16, #17, #20) A rectangular swimming pool measuring 10 m by 4 m is surrounded by a deck of uniform width. The combined area of the deck and the pool is 135 m 2. What is the width of the deck? I. Draw a picture & label the given information. II. Write a 'let statement' for the width of the deck III. Write and simplify an expression for the combined area of the pool. IV. Solve the possible values for x. (discard any inadmissible values w/ explanation). V. Look back to the original question, complete any necessary calculations then write a final statement w 4 + 2w 4

5 II. Numbers (key words: sum, consecutive integers, difference, squares...) The sum of the squares of two consecutive integers is 685. What could the integers be? (list all possibilities) I. Write a 'let statement' for the two integers II. Write and simplify an expression for the sum. IV. Solve the possible values for x. (discard any inadmissible values w/ explanation). V. Look back to the original question, complete any necessary calculations then write a final statement. 5

6 III. Projectile Motion (football kick, rocket, cliff diver...) Sally is standing on the top of a river slope and throws a ball. The height of the ball at a given time is modeled by the function h(t) = 5t t + 10, where h(t) is the height in metres and t is the time in seconds. a) How long is the ball in the air, to the nearest tenth of a second? b) How high is the ball after 4 seconds? c) When will the ball be 10m above the ground? d) What is the maximum height of the ball? Keep in mind: i) Object hits ground when the height = 0 m. ii) If solving for "when" (the time) then need a height (h), if solving for a "how high" (height) then need a time (t). iii) Object reaches max height at the vertex! (not necessarily at the halfway point if object has an initial height iv) Initial height of object can be found at t=0 s Sally must be a super hero to have an arm that allows a ball to reach a maximum height of 55 m at a time of 3 s after throwing it from a cliff that is 10 m in height. You will get the same answer if you complete the square: see next page 6

7 Completing the Square d) Find the max height of the ball Vertex: (3, 55) Therefore, the ball reaches a maximum height of 55 m, 3 seconds after Sally throw it. (more likely to be that Sally launched a water balloon from a catapult or that she is a Super Hero!) 7

8 IV. Profit (could be any equation that has a max including a population) The profit of a skateboard company can be modeled by the function P(x) = x 14x 2, where P(x) is the profit in thousands of dollars and x is the number of skateboards sold, also in thousands. a) What is the maximum profit the company can earn? b) Determine when the company is profitable by calculating the number of skateboards that must be sold to break even. 8

9 HOMEWORK Page 130 #16, 17, 20, 21, 29, 30 9

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