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Quadratic Equations and Problem Solving MATH 018 Combined Algebra S. Rook Overview • Section 6.7 in the textbook: – Solving Quadratic word problems – Applying the Pythagorean Theorem 2 Solving Quadratic Word Problems 3 Solving Quadratic Word Problems • Object is to extract a quadratic equation from the word problem • Solve by factoring • Takes practice 4 Solving Quadratic Word Problems (Example) Ex 1: Set up a quadratic equation and solve: a) The difference of the square of a number and the number itself is thirty b) The sum of four times the square of a number and eight times the number itself is negative three c) Two consecutive odd integers whose product is 63 5 Applying the Pythagorean Theorem Applying the Pythagorean Theorem • Pythagorean Theorem: given a right triangle with legs a & b and hypotenuse c, the following relationship exists: a2 + b2 = c2 – It does not matter which of the legs is a and which is b – The hypotenuse, c, is the longest side AND is ALWAYS opposite the 90°-angle • When solving problems with right triangles, it is often helpful to draw a picture 7 Applying the Pythagorean Theorem (Continued) • Bear in mind the domain of the problem (i.e. what the problem is addressing) – Even though some solutions of an equation may be mathematically correct, they may not make sense in the context of the problem • What is the domain of the Pythagorean Theorem? – What do you know sign-wise about the domain? 8 Applying the Pythagorean Theorem (Example) Ex 2: A 10 foot ladder is leaning on a building which is perpendicular to the ground where the top of the ladder (vertically) extends two feet more than across the ground (horizontally). Set up an equation and find how many feet the ladder extends off the ground (vertically) 9 Applying the Pythagorean Theorem (Example) Ex 3: One leg of a right triangle is 4 millimeters longer than the smaller leg and the hypotenuse is 8 millimeters longer than the smaller leg. Find the lengths of the sides of this triangle 10 Summary • After studying these slides, you should know how to do the following: – Solve quadratic word problems – Solve problems involving the Pythagorean Theorem • Additional Practice – See the list of suggested problems for 6.7 • Next lesson – Simplifying Rational Expressions (Section 7.1) 11