Warm-Up Exercises. Daily Ho ework Quiz for use after Lesson 5.2, pages x = 0. Solve the equation.

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1 ! Date Warm-Up Exercises For use before Lesson 5.3, pages Availa le as a tran parency Solve the equation. 1. 5x - 3 = = ? Find the value of y when = 0,1, and y = -16* y = - ISx Daily Ho ework Quiz for use after Lesson 5.2, pages actor the quadra ic expression * x2 + 4.x * lo + 1 Solve x = x2 + llx + 3 = 2x2-3x Find the zeros of y = 8x2 18x. Chapters -Resource Book Copyright McOougal Utteiitac. A rights reserved.

2 Date Application Lesson Opener For use with pages Available as a transparency A number r is called a square root of s if r2 s. The notation 5 represents the positive s uare root of s. According to the Vickers scale, the hardness H of a mineral is determined by the formula Hd2 = 1.89, whe e d is the, de th. (in millimeters) of an indentation formed by hitting the ineral with a yra id-sha ed di nond. If you know H, you can use a square root to solve the equation for d. Here is how to find the de th of indentation for a mineral whose hardness is 131: Hd2 = d2= 1.89 d2=~ 131 d = ± Write the formula. Substitute 131 fo H. Divide each side by 131. Take square roots of each side. Use a calculator to find the positive square root. The depth of an indentation is about 0.12 millimeter. Use a calculator to find the depth of an indentation for each mineral. Round to the nearest hundredth of a millimeter. Lesson Co per: H = Galena: fl = 80. _ 3. Platinum: H = Gold: H Hematite: H = Graphite: H = 12 Copyright McOougal Littell Inc. Chapters Resource Book

3 * Practice A For use with pages Date Si plify the expression Vn loo 9. vf 8- Vir l 7? >" i /f Solve he equation ? x2 ~ 36 = = = xz *? = N)N> I U> II -* 3. a:2 + 2 = Jt S 2 1 = ~ il = *2 + 5 Find the time i takes an object to hit the ground when it is ropped from a height of $ feet. Use the falling-object mo el ft s-let2 + s = j = 160 * 30. s = 320 Use the Pythagorean theorem to fin x. Roun your ans er to the nearest hun redth. 33. Cost of a New Car From 1970 to 1990, the average cost of a new c r, C (in dollars), can be approximated by the model C = 30.5{2-4192, here t is the number of years since During which year was the average cost of a new car $12,000? Copyright McOougal Littel!!nc. Chapters Resource Book 41

4 < -: j i i t. f oirnpmy p ify fhe tneexpression. 4 g, 2 jg Solve the e uation. Practice B For use with pages VfSO 5. s IS * 5 / / 3 * V x2-81 == x = fx2-~ 8 =* = 3x (x2 + 4) = {x -f 3) (x--2)2 + 4 = 22. (2x -- 3)2 = f(x--4)2 = 8 3. V63 Date 6. lo B Sx1-180 = j 2 ~ 5 = (jc2-1) = (3 c + l)2 36 = l)'z-16 0 c w V) ".5» 25. Falling Object Use the falling-object model A = -16/2 + j where? is measured in seconds and h is measured in feet to find die time required for an object to reach the ground from a height of s = 100 feet and s feet. Does an object that is dropped from twice as high take twice as long to reach the ground? Explain your answer. 26. Track Registrations From 1990 to 1993, the number of truck registra tions (m millions) in the Unite States can be ap roximated by the model R = 0.29/2-45 ere t is t e u ber of ye rs si ce During, hich year were ap roximately million trucks re istered? Short Cut Suppose your house s on a large comer lot. The children i the neighbor ood cut across our la n, as shown in the figure at the right. The distance across the lawn is 35 feet. 27. Use t e Pythagorea theorem to find x. 28. Fin the distance the children would ave to travel if they did not cut across our la n. 29. How ma y feet do the children save by ta ing the short cut? Chapter s Resource Book Copyrigh McDougai Utteii Inc. All right reserved.

5 » - ' Reteaching with Practice DATE:,Yl ll i H : For use with pages \ Solve quadratic equations by finding square roots and use qua ratic e uations to solve real-life problems fcv Vocabulary If &2 = a, then bis a. square root of a. A positive number a has two square roots, and - a The symbol r- is a radical sign, a is the radic n, and Ja is a radical. Rationalizing the denominator is the rocess of eliminating square roots in the denominator of a fraction. Using Properties of Square Roots Simplify the expression. a. V99 = V9 VTT = 3 TT V 25 5 b. 6* 8 = 48 yi6*v = 4V3 d _ 6 5 _ 6V5 S 5 * Vs 5 Exercises forjexample 1 Simplify the expression. 1. V60 2. V2 * IS Solving a Quadratic Equation to w Solve 4 6 So ution ;C.. 0 V) Write original equation. r - ; 6 14 Add 4 to each side. 2 = 84 X = ±V84 X= ±2'V2l Multiply both sides by 6. Take square roots of both si es. Simplify. The solutions are 2V2T and 2V2T. ExercisesforJE 2 Solve the equation. 4. 4x2 5 = V ~ = 33 Cha ters Res urce Book Copyright McDoufial UttplHne

6 LESSON 0.0 Reteaching with Practice CONTINUED» For use with pages Date Solving a Quadratic Equation Solve 5(x-7)2 = ( 7)2 = 135 Write original equation. (x - 7)2-27 Divide both sides by 5. x-1 - ±V! Take the square roots of both sides. x l~± 3>/3 limplif. x l± 3 /3 Add 7 to both sides. The sol tions are 7-3-v/3 nd 7 3 /3. Exercises for Examftle 3 Solve the equation. 7. (y - 3) (r - 8) (w - l)2 = (x 3)2 = (x 3)2 = {z 4-3)2 5 Modeling a Falli g Objects Height with a Quadratic Functio A person is trapped in a building 120 feet above the ground a d wants to land on a rescue team s air cushon. How long before the person reaches safety? Solution Use the falling object model h~ - 16t2 + h0, where A is the height (in feet) of the object after t seconds and h0 is the object s initial height. 0 = -16*2-120 Substitute 1 0 for h0 and 0 for h. 120 = 16 2 Subtract 120 from each side. 120 = r2 Divide each side by -16, 16 Lesson 5-3 Take positive square root. 2,7 *= t Use a calc lator. The person will reach safety in about 2.7 seconds. misesfyrgantgled 13. A coyote is sta ding on a cliff 254 feet above a roadrunner. If the coyote drops a boulder from the cliff, how much time oes the roa runner have to move out of its way? 14. An apple falls from a branch on a tree 30 feet abov a man sleeping un e eath. When will the apple strike the man? Copyright McDougal Littell Inc.. Chapter ResqurceBook