April 11, 2012 Solving Equations using Quadratic Techniques Warm-up: Use a math interpretation to describe your spring break or life in general. You could use numbers, symbols, math operations, expressions, equations, equations of graphs, etc. Then write your interpretation underneath. For example, mine would be: y = |x |“My life is V- shaped, sometimes live events bring me down, but family and friends usually help bring me up.

Finals For today’s lesson, make sure you remember how to solve for #1 and #4

7.3 Solving Equations using Quadratic Techniques Example 1: How to Rewrite the expression in quadratic form: x 4 – 13x st check for a GCF! Then factor it out. 1. Take the power of the middle value. 2. Think to yourself… x2x2 “If I square x 2, will it equal x 4 ?” YES! If the answer to #2 is “YES!”, then, let x 2 = u Rewrite the expression using x 2 : (x 2 ) 2 – 13x Then rewrite the expression using u: u 2 – 13u + 36 Thinking process…

Practice writing an expression in Quadratic Form 1.x 4 – 17x a 8 – 10a m 5 + 6m 4 + 5m 3 Don’t forget! 1 st check for a GCF, then factor it out.

Solving using Quadratic Form Example 2: Solve: x 4 – 13x = 0 (x 2 ) 2 – 13x = 0 u 2 – 13u + 36 = 0 (u – 9)(u – 4) = 0 u – 9 = 0 and u – 4 = 0 u = 9 u = 4 x 2 = 9 x 2 = 4 x = ±3 x = ±2 1. Let x 2 = u 2. Rewrite in Quadratic Form 3. Factor 4. Solve for u 5. Replace u with x 2 6. Solve for x

Solve using Quadratic form 1.x 4 – 17x = 0 2. a 8 – 10a = 0 3. m 5 + 6m 4 + 5m 3 = 0 Don’t forget! 1 st check for a GCF, then factor it out.