1. 5.2 Graphing Quadratics Simplifying Radicals

2. 5.2 Graphing Quadratics MT5 will be a hard test that will require many of your hard earned math skills. In this lesson, you will be preparing yourself for working with the Quadratic Formula… The Quadratic Formula is used to find the x intercepts (zeros) of a Quadratic Equation. In this lesson, we will learn a technique that will simplify the number under the Radical Symbol (Square Root Sign). This will help us later when we have to find zeros using the Quadratic Formula.

3. 5.2 Graphing Quadratics Perfect Squares escape Radicals very easily. Here are some perfect squares that you should already know… 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 And so on…(You should memorize up to 15 x 15) This is probably review, but let’s cover the basics anyway. 9 = ± 3 16 = ± 4 49 = ± 7 Notice the answer to a simplified square root is both Positive and Negative! Why?

4. 5.2 Graphing Quadratics You can probably do the easy square roots in your sleep! Sometimes, though, what is inside the radical is not a perfect square. Here is an example… 12 12 is not on the list of perfect squares; how do we simplify this? The first thing to do is to break down 12 into its prime numbers. We use Factor Tree for this… 12 4 3 2

5. 5.2 Graphing Quadratics Since 12 = 3 x 2 x 2, this is what we put under the radical The most important thing we have to remember is that “Pairs Escape; Singles Don’t”. 12 4 3 2 3*2*2 Our next step is to circle the numbers that have pairs… 3*2*2 The pair of “2’s” escape the radical and become one “2”. The “3” stays on the inside. ± 2 3