N6.+Identify+the+key+points+of+a+quadratic+function,+including+the+maxium+or+minimum,+y-intercept,+and+x-intercepts,+if+they+exist

**1. What you need to understand.**

or The letters a, b, and c are real number.
 * You need to understand what a quadratic function is, and where the key points are if they exist.
 * A quadratic function is
 * a > 0, **__a is not equal to zero__**. If a is (+) then it makes a happy graph, if (-) then is makes a sad graph.
 * b takes the graph off center
 * c is the y-intercept
 * [[image:Screen_shot_2011-05-31_at_9.46.06_AM.png width="17" height="22"]]=makes it symmetric
 * the smaller a is the wider the graph is, and the larger a is the narrower the graph is

**Key Points:** Maxi mum/minimum

To find the max/min this is what you need to know:
 * This is the formula to find max/min or x=[[image:Screen_shot_2011-05-31_at_3.43.29_PM.png]]
 * Plug that formula into the quadratic function [[image:math2.jpg width="99" height="22"]]
 * After plugging this into the function f(x) =a (-b/2a) +b(-b/2a) + c
 * you will find the **__y-__** **__coordinate__** (x,y) <-

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">To find the x-intercepts and the y-intercept this is what you need to know:
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">You put 0 in for f(x) or y however you write the function will be like this.[[image:Screen_shot_2011-05-31_at_5.09.51_PM.png]]
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Then factor it. You will get something like this (_x+_)(_x+_)

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Let me show you an example. Suppose you have this function and you had to factor it. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">. This function wouldequal to this. (x+1)(3x+2)
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">After you factored this function. Now 0=(x+1) (3x+2)

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">The y-intercept is easier to figure out. The letter c is the y-intercept, let x=0, then whatever the # is for c then that's the y-intercept. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Let me use the same equation from above. , then put 0 in for x. Everything equals 0 except for the 2, for the y-intercept is 2.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**2. Example.** <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px; line-height: 23px;">Example 1. Graph the function find the max/min, then find the x-intercepts. min= -1.5, -0.5 __<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: 23px;">X-intercepts __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px; line-height: 23px;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: 23px;">I have to factor this function[[image:Screen_shot_2011-06-06_at_4.28.08_PM.png]]
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px; line-height: 23px;">f(x)=(2x+2)(x+2) is the factored form. I checked my self by expanding it again.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px; line-height: 23px;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: 23px;">The x-intercepts are -1 and -2


 * 3. Misunderstandings or Mistakes.**
 * Sign errors ( might forget to carry the signs to the next equation)
 * getting mixed up with figuring out Max/min and x,y-intercept
 * Arithmetic erros

To prevent mistakes- **__ALWAYS DOUBLE CHECK YOUR WORK!__**


 * 4. For more information.**
 * http://dl.uncw.edu/digilib/mathematics/algebra/mat111hb/pandr/quadratic/quadratic.html
 * http://www.showmethemath.com/Concepts_Explained/quadraticsAndFactoring/notes_QuadraticFunctions.pdf
 * Addison-Wesley Algebra Book. Unit 12 Lesson 1 pg. 514-517