Created by Judy L. McDaniel

Be sure to write a quadratic equation in before using most methods for solving. (not necessarily for the Square Root Prop.) Only solutions make sense in most - situations. As we have noticed, Quadratic Equations can have,, or solutions. Form Real Positive Standard World onetwono

Review of best methods to use to solve Quadratic Equations: Method When to Use: GraphingIf a quick estimate is needed or a Graphing Calculator is available. Square Root Prop.If the equation is in the form ax 2 + c = 0, (no “bx” term) FactoringIf the equation factors easily x 2 + bx + c = 0, (a = 1) or ax 2 + bx = 0 form Quadratic FormulaIf the equation does not factor easily ax 2 + bx + c = 0 or is not factorable at all, (a ≠ 1)

 The can help us determine how many solutions to expect in our final answer.  It is the expression “under” the sign. ( ) If the expression is, expect answers. ( b 2 – 4ac > 0) If the expression is, expect answer. ( b 2 – 4ac = 0) If the expression is, expect answers. ( b 2 – 4ac < 0) {No REAL Solutions) Discriminant Radical b 2 – 4ac Positive Negative Zero 2 1 0

Problem 3 Choose an Appropriate Method Which method would you choose to solve each quadratic? Explain your reason. A. 3x 2 – 9 = 0 B. 6x x – 17 = 0 C. x 2 – x – 30 = 0 D. x 2 – 5x + 3 = 0 E. –3x = 0 Square Root Prop. Quadratic Formula Factoring OR ax 2 + c form x 2 + bx + c form ax 2 + bx + c form Factoring x 2 + bx form Not Factorable ax 2 + c form

Problem 4 Use the Discriminant (to Determine the Number of Solutions) Find the number of roots each equation has. Then, solve the equation. A. 2x 2 + 7x – 16 = 0 B. 3x 2 + 4x + 8 = 0 a = b = c = Look for 2 REAL Solutions! 2 There is no perfect square root of 177 so this is your answer 7 (7) 2 – 4(2)(–16) 3 – – (–128) 177 (a positive number so……) 8 a = b = c = (4) 2 – 4(3)(8) 16 – (96) –80 (a negative number so……) There are NO REAL Solutions! {1.576, –5.076} OR

Now You try: 2x 2 – 8x + 5 = 0 a = b = c = –8 2 5 There is no perfect square root of 24 so this is your answer {3.225, 0.775} OR (–8) 2 – 4(2)(5) 64 – (40) 24 (a positive number so……) There are 2 REAL Solutions! Not What you have? Let’s take a look… {3.225, 0.775}