Solve x 2 + bx + c = 0 by Factoring Chapter 4 Section 3

Lesson Essential Question How can factoring be used to solve quadratic equations?

Ex 1: Factor trinomials of the form x 2 + bx + c 1) x 2 – 9x + 202) x x ) x 2 – x – 124) x 2 + x – 42 5) x 2 + 3x – 126) x 2 + 2x – 63 7) x 2 – 3x – 188) n 2 – 3n + 9 9) x 2 – 9x – 5

Ex 2: Factor with Special Patterns 1) x 2 – 49 2) d d ) z 2 – 26z ) x 2 – 9 5) q 2 – 1006) y y ) w 2 – 18w + 818) m 2 – 121

Ex 3: What are the roots? Roots – the solutions of a quadratic equation 1) x 2 – 5x – 36 = 0 2) x 2 – x – 42 = 0

Ex 4: Find the zeros of quadratic functions 1) y = x 2 – x – 12 2) y = x x ) y = x 2 + 5x – 14 4) y = x 2 – 7x – 30 5) y = x 2 – 10x ) y = x 2 + 3x – 28 7) y = x 2 – 4x + 4

Ex 5: Application Problems 1) A town has a nature preserve with a rectangular field that measures 600 meters by 400 meters. The town wants to double the area of the field by adding the same distance of land x to the length and width of the field. Find the new dimensions of the field.

Ex 5: Application Problems 2) You have a rectangular vegetable garden in your backyard that measures 15 feet by 10 feet. You want to double the area of the garden by adding the same distance x to the length and width of the garden. Find the value of x and the new dimensions of the garden.

Ticket Out the Door How can factoring be used to solve quadratic equations when a is equal to one?