Warm up 5-59. BACKYARD SOLUTIONS Draw a diagram and write an equation to represent each scenario below.  Solve the equation, and then explain whether the solutions make sense. Ernie is going to install a square hot tub in his backyard.  He plans to add a 3-foot-wide deck on two adjacent sides of the hot tub.  If Ernie’s backyard (which is also a square) has 169 square feet of space, what is the largest hot tub he can order? Gabi is creating a decorative rock garden that will cover 12 square feet of her back yard, including its frame.  She plans to build a 6-inch wide wood frame around the rock garden to keep the rocks in place.  If the framed rock garden is square, how much area will Gabi need to cover with decorative rocks? (x + 3)2 = 169 |x + 3| = 13 x + 3 = 13 or x + 3 = -13 x = 10 or x = -16 10 feet x 10 feet hot tub (x + 1)2 = 12 |x + 1| =  12 x + 1 =2 3 or x + 1 = -2 3 x = -1+ 2 3 or x = -1- 2 3 x = 2.5 or x = -4.5 2.5 feet x 2.5 feet rock garden Wood frame Rock garden .5 ft Warm up

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5.2.1 Perfect Square Equations HW: 5-65 through 5-70 5.2.1  Perfect Square Equations January 25, 2016

Objectives CO: SWBAT solve quadratic equations in perfect square form and express their solutions in exact and approximate forms. LO: SWBAT explain how many solutions a quadratic equation written in perfect square form has.

team What method did you use to solve each equation? |x – 1| = 2 5-60. In problem 5-59, did you notice anything special about the forms of the equations you wrote?  Did you use the Zero Product Property to solve your equations, or were you able to solve them a different way? Without rewriting, determine the value(s) of x that make(s) each equation true.  a.     (x – 1)2 = 4 b.     (x – 1)2 = 0 c.     (x – 1)2 = –4 |x – 1| = 2 x – 1 = 2 or x – 1 = -2 x = 3 or x = -1 |x – 1| = 0 x – 1 = 0 x = 1 No solution because no number times itself will ever give a negative. What method did you use to solve each equation? team

5-61. The quadratic equation (x – 3)2 = 12 is written in perfect square form.  It is called this because the expression (x – 3)2 forms a square when built with algebra tiles. Solve (x – 3)2 = 12.  Write your answer in exact form (or radical form).  That is, write it in a form that is precise and does not have any rounded decimals. (x – 3)2 = 12 |x – 3| = 12 x – 3 = 2 3 or x – 3 = - 2 3 x = 3 + 2 3 or x =3 - 2 3 How many solutions are there? 2 The solution(s) from part (a) are irrational. That is, they are decimals that never repeat and never end.  Write the solution(s) in approximate decimal form.  Round your answers to the nearest hundredth.  x ≈ 6.46 or –0.46 team

5-62. THE NUMBER OF SOLUTIONS The equation in problem 5-61 had two solutions.  However, in problem 5-60, you saw that a quadratic equation might have one solution or no solutions at all.  How can you determine the number of solutions to a quadratic equation? With your team, solve the equations below.  Express your answers in both exact form and approximate form.  Look for patterns among the equations with no solution and those with only one solution.  Be ready to report your patterns to the class.  a.     (2x – 3)2 = 49 b.     (7x – 5)2 = –2 c.     (x + 4)2 = 20 d.     (5 – 10x)2 = 0 e.     (x + 2)2 = –10 f.      (x + 11)2 + 5 = 5 x = –2 or 5 2 solutions No solution x = 3 + 2 3 or 3 - 2 3 x ≈ 0.47 or –8.37 2 solutions x = ½ 1 solution No solution x = -11 1 solution 2 solutions → squared equals positive 1 solution → squared equals zero No solution → squared equals negative 1=a, 2=b, 3=c, 4=d, E&f first to finish, Then Share