Week 6-Pre Calc 11 | Katelyn's Blog

This week in Pre Calc 11we learned the 3 ways to solve quadratic equations. The 3 ways are;

1. Factoring

2. Completing the squares

3. Using quadratic equation

Factoring: this is the easiest way to solve quadratic equations

Example:

$x^2-9x-22=0$ > Start off with your equation

$x^2-11x+2x-22=0$ > find your 2 numbers that multiply to 22 and add to -9 (-11,2)

$(x-11)(x+2)$ > factor by grouping common term (look at week 5 post)

$x=11 x=-2$ > when you have your 2 bracketsyou take the opposite of both numbers and those would be what x equals, in this case the opposite of -11 is 11 and the opposite of 2 is -2

Completing the square: $(b/2)^2$

Example:

$x^2+4x+1=0$ > start with your equation

$(x^2+4x+4)+1-4=0$ > separate $x^2+4x$ and +1 by using brackets, from there you take whatever number is b (4), divide it by 2 and then square it. For this equation our number will be 4, you then put that number beside 4x and you also put the opposite of that number (-4) and put it beside 1

$(x+2)^2-3=0$ > you foil what’s in the bracket and take the copy bracket turn it into $(x+2)$ which is the same as (x+2)(x+2). You also solve outside the bracket so 1-4=-3