Solving Quadratics by Factoring Unit 2 – Day 3

Warm-Up Write an equivalent expression for each of the problems below: 1) (x + 2)(2x2 +3x - 4) 2) (x - 9)2 Describe the transformation from the quadratic parent function: 3. 10 minutes End

HW Check

Today’s Objective Students will use algebraic reasoning (algebra) to solve a quadratic equation.

Finding Zeros of Quadratics Investigation Today we will find the relationship between two linear binomials and their product which is a quadratic expression represented by the form . First we will generate data and the look for patterns. Time Keeper: 45 minutes Resource Manager: Solving Quadratics Algebraically Investigation Worksheets Reader: Read problems out loud to group Spy Monitor: Check in with other groups if you are stuck

Part I: Generate Data Use the distributive property to multiply the following binomials, and then simplify. 1. x2 + 8x + 15 2. x2 + 2x – 8 3. x2 – 3x + 2

Part I: Generate Data Use the distributive property to multiply the following binomials, and then simplify. 1. → x2 + 8x + 15 2. → x2 + 2x – 8 3. → x2 – 3x + 2 Where do you expect each of the above equations to “hit the ground”? 1. x = -3, x = -5 2. x = -4, x = 2 3. x = 1, x = 2

Remember: You can find where the graph “hits the ground” using your calculator and finding the intersection with the x-axis. These are called Zeros, Roots, or Solutions. You can also find them by setting each factor equal to zero and solving. We can do this because of the Zero Product Property.

Part II: Organize Data

Part III: Analyze Data Answer the following questions given the chart you filled in above 1. Initially, what patterns do you see? 2. How is the value of “a” related to the factors you see in each problem? 3. How is the value of “b” related to the factors you see in each problem? 4. How is the value of “c” related to the factors you see in each problem?

Factoring Factoring is working backwards from the trinomial to the binomial. The goal of factoring is to help us solve a quadratic by finding the x-intercepts

Part IV: Application

Difference between factor and solve? If asked to factor, your answer should be the form (x + #)(x + #) If asked to solve, you must first factor then set each factor equal to zero.

Recap: Factor: To find the zeros: Your equation must be equal to 0. Factor the quadratic Set each factor equal to 0. Solve each factor for the variable.

HOmework Complete the factoring worksheet