3.1 Notes: Solving Quadratic Equations By graphing and square roots

What does it mean to “solve?” When we are solving a quadratic equation, we are finding the x- intercept(s), real and non-real, that would be on our graph. There are at least five methods for solving, today we will look at two methods.

Solving by graphing Whether we graph by hand or on the graphing calculator, we are graphing a quadratic equation and looking for the place(s) where the graph touches the x – axis. Before we graph, we must make sure our equations are equal to 0!

Let’s try some: 1) x 2 – x – 6 = 02) -2x 2 – 2 = 4x 3) x 2 + 3x – 10 = 04) 2x = 12x 5) x 2 = 6x - 20

Solving by Square Roots We can solve by using backward order of operations (SADMEP), which would use square roots. The “b” term MUST be missing in order to do this (of ax 2 + bx + c) ALL roots MUST be SIMPLIFIED! Don’t forget, negative roots mean we have to pull out “i”

Let’s try some: 1) 4x 2 – 31 = 492) 3x = 03) (x + 3) 2 = 5 4) 2(x – 4) 2 = -5 5) -2x = -6

HW: P. 99 #3 – 11 odd; 13 – 17 odd CH 3 QUIZ Friday 9/11