www.mhhe.com/messersmith 107) Let f (x) (x 3)2. Find x so that f (x) 49. 108) Let g(t) (t 5)2. Find t so that g(t) 12. Solve each problem by writing an equation and solving it by completing the square. 109) The length of a rectangular garden is 8 ft more than its width. Find the dimensions of the garden if it has an area of 153 ft2. 110) The rectangular screen on a laptop has an area of 375 cm2. Its width is 10 cm less than its length. What are the dimensions of the screen? 106) Salma is fl ying a kite. It is 30 ft from her horizontally, and it is 40 ft above her hand. How long is the kite string? ft ft R1) Why must the coeffi cient be “1” before you use the square root property? R2) Can you think of a real-life situation where you may need to use the distance formula? R3) What do you fi nd most diffi cult about completing the square? After you complete the square, which method do you use next? 10.2 The Quadratic Formula What are your objectives for Section 10.2? How can you accomplish each objective? 1 Derive the Quadratic Formula • Understand where the quadratic formula comes from. • Learn the quadratic formula. Practice writing it several times in your notes. 2 Solve a Quadratic Equation Using the Quadratic Formula • Know how to write a quadratic equation in standard form. • Be able to identify a, b, and c in the quadratic formula. • Complete the given examples on your own. • Complete You Trys 1 and 2. 3 Determine the Number and Type of Solutions of a Quadratic Equation Using the Discriminant • Write out all the possible types/number of solutions for a discriminant in your notes. • Complete the given example on your own. • Complete You Try 3. 4 Solve an Applied Problem Using the Quadratic Formula • Read the problem carefully. • In a motion equation, be able to determine if you are solving for height (h) or solving for time (t), if applicable. • Review the Pythagorean theorem. • Complete the given example on your own. • Complete You Try 4. SECTION 10.2 The Quadratic Formula 623
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