window._wpemojiSettings = {"baseUrl":"https:\/\/\/images\/core\/emoji\/2\/72x72\/","ext":".png","svgUrl":"https:\/\/\/images\/core\/emoji\/2\/svg\/","svgExt":".svg","source":{"concatemoji":"http:\/\/\/wp-includes\/js\/wp-emoji-release.min.js?ver=4.6.5"}}; !function(a,b,c){function d(a){var c,d,e,f,g,h=b.createElement("canvas"),i=h.getContext&&h.getContext("2d"),j=String.fromCharCode;if(!i||!i.fillText)return!1;switch(i.textBaseline="top",i.font="600 32px Arial",a){case"flag":return i.fillText(j(55356,56806,55356,56826),0,0),!(h.toDataURL().length<3e3)&&(i.clearRect(0,0,h.width,h.height),i.fillText(j(55356,57331,65039,8205,55356,57096),0,0),c=h.toDataURL(),i.clearRect(0,0,h.width,h.height),i.fillText(j(55356,57331,55356,57096),0,0),d=h.toDataURL(),c!==d);case"diversity":return i.fillText(j(55356,57221),0,0),e=i.getImageData(16,16,1,1).data,f=e[0]+","+e[1]+","+e[2]+","+e[3],i.fillText(j(55356,57221,55356,57343),0,0),e=i.getImageData(16,16,1,1).data,g=e[0]+","+e[1]+","+e[2]+","+e[3],f!==g;case"simple":return i.fillText(j(55357,56835),0,0),0!==i.getImageData(16,16,1,1).data[0];case"unicode8":return i.fillText(j(55356,57135),0,0),0!==i.getImageData(16,16,1,1).data[0];case"unicode9":return i.fillText(j(55358,56631),0,0),0!==i.getImageData(16,16,1,1).data[0]}return!1}function e(a){var c=b.createElement("");c.src=a,c.type="text/java",b.getElementsByTagName("head")[0].appendChild(c)}var f,g,h,i;for(i=Array("simple","flag","unicode8","diversity","unicode9"),c.supports={everything:!0,everythingExceptFlag:!0},h=0;h var base_url_sociable = '' /* */ // window.google_analytics_uacct = "pub-1491670887385744"; var analyticsFileTypes = ['']; var analyticsSnippet = 'disabled'; var analyticsEventTracking = 'enabled'; (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'','//','ga'); ga('create', 'UA-10665245-1', 'auto'); ga('send', 'pageview'); var $j = jQuery.noConflict(); $j(document).ready(function(){ $j('#container-4 > ul').tabs({ fx: { opacity: 'toggle', duration: 300 }}); });

Seven Weeks to Precalculus: Day 1 – Quadratic Equations

May 7th, 2012 | By | Category: Featured Article, snewz

General form of quadratic equations:

a, b, and c are all elements of the set of real numbers (a, b, & c ∈ of ℝ)

a ≠ 0

ax2: Quadratic Term

bx: Linear Term

c: Constant Term

Three fundamental truths of quadratic equations:

  1. Quadratic equations are also called polynomial equations (exponential equations whose exponents are raised to integers (positive whole #’s)).
  2. The solutions are the values that make the equation true
  3. There are two solutions to a quadratic equation
    1. Two real solutions (ex: x2-9=0; x=±3)
    2. Two complex solutions (ex: x2+9=0; x=±3i)
    3. One real solution with multiplicity 2 (ex: x2-2x+1=0=(x-1)2; x=1±0)

Methods for solving Quadratic Equations:

  1. Factor the quadratic equation into linear factors (zero product property)

“If a times b = 0, this implies a=0, b=0, or a&b = 0.”

  1. Square Root Property: Rearrange terms so that your variable squared is equal to a number.
    1. x2=k
    2. x=±√k
    3. Completing the square: Rearrange terms and add a value to both sides of the equation so that one factor with multiplicity 2 equals a real number.

  1. Quadratic Formula: Derived from ax^2+bx+c format. See link for step-by-step proof: Khan Academy Quadratic Formula Proof



Be Sociable, Share!

Leave a comment »

  1. It’s remarkable to visit this website and reading the
    views of all friends regarding this article, while I am also zealous of getting knowledge.

  2. Greetings! This is my first visit to your blog! We are a collection of volunteers and starting a
    new initiative in a community in the same niche. Your blog provided us valuable information to work on. You have done a extraordinary job!

Leave Comment