Name: _______________________ Class: __________ Date:_____________ Math SL: Quadratic Word Problems 1F and Quadratic Optimization 1G Warm-­‐up 9
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1. Determine the fourth term in the expansion of ⎜ 2x + 2 ⎟ .
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2. Solve for x: sin(x+0.5) = 0.25x
1 1F Problem Solving with Quadratics
Basically we are now dealing with real life situations where quadratic equations are used to model a quantity such as an area, speed, etc. Example 1: The product of two consecutive even numbers is 360. Find the numbers. Step 1: If the information is given in words, translate it into algebra using a variable such as x for the unknown. Write down the resulting equation. Step 2: Solve the equation using a suitable method. Step 3: Check your solutions to see if they are reasonable. Step 4: Write your final answer in a sentence. Example 2: A uniform concrete path is paved around a 30 m by 40 m rectangular lawn. The area of the concrete is one quarter of the area of the lawn. Find the width of the path. 2 1G Quadratic Optimisation
These problems are similar to the last section, except you will be finding the maximum or minimum value of a quadratic function. This is called optimisation. Example 1: A rectangular plot is enclosed by 200 m of fencing and has an area of A square meters. Show that: a. A = 100x − x 2 where x m is the length of one of its sides. b. The area is maximized when the rectangle is a square. 3 Example 2: A manufacturer of pot-­‐belly stoves has the following situation to consider. If x are made per week, each one will cost 50 + 400
dollars and the total receipts per x
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week for selling them will be 500x − 2x 2 dollars. How many pot-­‐belly stoves should be made per week in order to maximize profits? Hmwk#22 1F Problem solving with quadratics pg 45: #3, 7, 8, 10, 12, 15 1G Quadratic optimisation pg 47: #2, 4, 5, 7, 8 4