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Name: ________________________ Mr. Art Date: _____________ Period: ___________ Review # _____ Quadratic Equations Algebraically Part I: Linear vs. Quadratic Equation Graphically 1) Linear Equation: 7th grade Degree: __1__ Graph: ___Line________________ 2) Quadratic Equation: 8th grade Algebraically Graphically Degree: ___2___ Graph: ____Parabola______________ * When solving quadratic equations we are looking for the zeros, roots or solutions of the equation. This is where the parabola (graph) intersects the x-axis. y = x2 - 3x - 28 Directions: Complete the table below. Equation Degree Type of Equation 3x + 7 = 10 1 Linear x2 + 6x + 5 = 0 2 Quadratic 2 Quadratic 1 Lesson 6-1: Quadratic Equations = 0 & Lesson 6-2: Quadratic Equations 0 Steps: 1) Standard Form: ax2 + bx + c = 0 (Set equal to zero) x2 term must be positive. Move all terms to the side where + x2 is. If you are given -x2, subtract it over to the other side of the equation to make it positive. 2) Factor completely 3) Set each factor equal to zero ("T" it off ) 4) Solve each equation for the variable 5) Solution Set (b/c we may have multiple solutions) 6) Optional Check (each solution) Checks: *Step 0: Distribute when you have a monomial times a binomial or trinomial. *This step is performed before step 1 if there are parentheses. x can equal zero, so keep x = 0 as one of your solutions. 2 cannot equal zero, so we reject it! *Remember: a Quadratic should 2 only have at most 2 solutions anyway. Lesson 6-3: Word Problems Let Statements: 1) When the problems provides variables No need for Let Statements 2) When you introduce the variable Let statements Easy: The square of a number is 64. Find the number. Faster but more risky method: Remember: (+8)(+8) = 64 and (-8)(-8) = 64. Medium: 10 Hard: 3 Lesson 6-4: Consecutive Integer Problems Consecutive: one after another Beginning of the problem End of the problem Let Statements: Positive or Negative Integers: 1) Consecutive Integers x, x + 1, x + 2 1) Positive Integers reject negative answers 2) Consecutive Even Integers x, x + 2, x+ 4 2) Negative Integers reject positive answers 3) Consecutive Odd Integers x, x + 2, x+ 4 NOT x, x + 1, x + 3! Easy Consecutive Integers: Easy Consecutive Odd Integers: 4 Medium Consecutive Odd Integers: Hard Consecutive Integers: 5 Lesson 6-5: Area Problems When using Algebra to solve Geometry problems, remember that dimensions can never be negative! Because of this, we always reject negative answers. 6 Lesson 6-6: Quadratic Proportions Steps: 1) Parentheses around binomials 2) Cross Multiply 3) Solve Easy: Medium: 7