Victory for the ACT Student Text 15e

224 • M ATH

60. Which of the equations that follow correctly describes the relationship between the values shown for x and y in the table below? x –2 –1 0 1 2 y 3 10 3 8 2 3 4 3 2 F. x y 3 2 6 + = G. x y 3 2 3 − = H. x y 3 3 6 + = − J. x y 6 4 7 + = K. x y 2 3 6 + = SOLVING QUADRATIC EQUATIONS AND RELATIONS

61. Which of the following is the solution set for x x 2 2 12 2 − = ? A. { , } 2 3 B. C. , 3 2 3 ' 1 D. , 2 3 2 ' 1 E. { , } 2 3 62. If x x 3 4 2 − = , then which of the following shows all possible values of x ? F. { , } 4 1 G. { , } 4 1 H. { , } 4 1 J. { , } 4 1 K. { , } 4 4 { , } 2 3 Throwback to Math Class Remember the quadratic formula: if , ax bx c 0 2 + + = then . x a b b ac 2 4 2 ! = − −

63. If x 2 + = , then which of the following shows all possible values of x ? A. {–5, 6} B. {5, 6} C. {5, –6) D. {–3, –10} E. {3, 10} 64. Which of the following is the solution set for x x 3 3 6 2 + = ? F. {1, –2} G. {1, 2} H. , 2 1 1 ' 1 J. , 2 1 3 1 ' 1 K. {–1, –2} 65. Which of the following is the solution set for x x 2 3 2 2 − = ? A. , 2 1 2 ' 1 B. , 2 1 2 ' 1 C. , 2 1 2 ' 1 D. {2, –2} E. {2, 4} x 30 11

Throwback to Math Class Follow these steps to solve quadratic equations. Step 1: Move all the terms to one side of the equation. The sum of the terms is then equal to zero: ax bx c 0 + + = 2 . Step 2: If the expression side of the equation is factorable, factor. Step 3: Set each of the factors equal to zero. Solve these equations for x , which has no more than two values.

Test-the-Test Test-the-test is a great strategy if the factors of a quadratic equation aren’t easy to identify and you have trouble with the quadratic formula. Simply plug the given answer choices into the quadratic ‡“—ƒ–‹‘ ‹ –Š‡ ‹–‡ •–‡ —–‹Ž ›‘— ϐ‹† ƒ ƒ•™‡” –Šƒ– ™‘”•Ǥ