advertisement

Algebra 1 SOL A.4 Completing the Square WS Mr. LUNT Name: ________________________________________ Date: 4/_______/16 Block: _______ Completing the Square Create a perfect square trinomial by completing the square: Given x 2 bx , find the “c” that completes the square by halving then squaring b Example: Find the “c” that completes the square in x2 + 6x + c b=6 half 6 (3) and square it (32) → c = 9 Solve Quadratic Equations by Completing the Square Example: Solve x 2 2 x 3 by completing the square 1) x 2 2 x 3 Make sure equation is in the format x 2 bx d , dividing through by a if necessary. 2) x 2 2 x 1 3 1 Complete the square on the expression on the left side of the equation, adding “c” to both sides 3) x 12 4 Write as a binomial square 4) x 1 2 Take square root of both sides, remembering both positive and negative roots 5) x 1 2 → x = -1, 3 Isolate x and solve Exercises: Write the perfect square trinomial as a binomial square. 1) x 2 2 x 1 2) x 2 14 x 49 3) x 2 24 x 144 Find the value of c that makes the expression a perfect square trinomial. Then write the expression as a square of a binomial. 4) x 2 8 x c 5) x 2 16 x c 6) x 2 4 x c 7) x 2 26 x c 8) x 2 18 x c 9) x 2 50 x c 10) x 2 9 x c 11) x 2 13x c 12) x2 1 xc 2 Algebra 1 SOL A.4 Completing the Square WS Mr. LUNT Page 2 Solve the equation by completing the square. Find your answers in simplest radical form (exact answers) as well as estimating to the nearest hundredth. 13) x 2 6 x 2 14) x 2 10 x 1 15) x 2 4 x 3 16) x 2 8 x 10 17) x 2 2 x 7 0 18) 2 x 2 24 x 42 0 19) x 2 6 x 40 0 20) x 2 3x 2 0 21) x 2 5 x 3 0 22) Find the value of x in the diagram by completing the square. 1 The area of a triangle is given by the formula A bh where b is 2 the base of the triangle and h is the height. 23) An arrow is shot in the air with an upward velocity of 64 feet per second from a hill 32 feet high. The height h of the arrow, in feet, can be found using the model h 16t 2 64t 32 where t is the time in seconds. a) Write an equation that you can use to find when the arrow will be 64 feet above the ground. b) When will the arrow be 64 feet above the ground? Round your answer(s) to the nearest hundredth.