Ch+5+0910


 * __ Roles of Wiki __ || __Student #1__ || __Student #2__ ||
 * Editor || Leann Murphy ||  ||
 * Multimedia || Evan Newcomer ||  ||
 * Text || Alisha Quigley || Rachel Robinson ||
 * Practice Problems || Joe Patterson ||  ||
 * <span style="background-color: #ff0000; color: #ffffff; font-family: Impact,Charcoal,sans-serif; font-size: 120%;">Career/Real Life App || <span style="background-color: #ff0000; color: #ffffff; font-family: Impact,Charcoal,sans-serif; font-size: 144%;">Christian Molander || ||

<span style="background-color: #000000; color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">Section 1: Graphing Quadratic Equations
<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">**Vocabulary** <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;"><span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">x = - b / 2a //
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">__<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">[[image:parabola.gif width="252" height="248" align="right"]] Quadratic Function__: //y = ax//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">² + bx + c //
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">__Parabola__: graph of a quadratic function; U-shaped
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">__Vertex__: lowest or highest point on the parabola
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">__Axis of Symmetry__: Vertical line that passes through the vertex;


 * Forms of Graphing & How to Graph them**

- __Standard Form__ <span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;"> <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">- __Vertex Form__
 * 1) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">//y = ax//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">² + bx + c //
 * 2) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">Direction of graph: upward if //a > 0//, downward if //a < 0//
 * 3) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">Axis of Symmetry: //x =// <span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">- b / 2a //
 * 4) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">Vertex: //(x,y)// X is found using, //- b / 2a// . Y is found by plugging the x-value back into the equation.
 * 5) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">Plot two points plugging x-values into the equation and using the axis of symmetry to plot them on the other side.
 * 1) //<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">y = a(x - h)² + k //
 * 2) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Direction of graph: upward if //a > 0//, downward if //a < 0//
 * 3) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Axis of Symmetry: //x = k//
 * 4) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Vertex: //(h,k)//
 * 5) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 16px;">Plot two points plugging x-values into the equation and using the axis of symmetry to plot them on the other side.

<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">- __Intercept Form__ <span style="color: #000000; font-family: arial,helvetica,sans-serif; line-height: 19px;">
 * 1) //<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">y = a(x - p)(x - q) //
 * 2) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Direction of graph: upward if //a > 0//, downward if //a < 0//
 * 3) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Axis of Symmetry: halfway between //(p,0)// and //(q,0)//
 * 4) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">Vertex: //( [axis of symmetry], y)// Y is found plugging the x-value back into the equation
 * 5) <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif; line-height: 19px;">X-intercepts: //p// and //q//
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">To turn Vertex or Intercept Form into Standard Form **
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">F O I L
 * <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">multiply the First term, Outer term, Inner term, and Last term, then combine like terms.

<span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">**Real Life Application** You can model real-life archeing objects with Parabolas, such as the golden gate bridge.

Graph y = 2x^2 – 8x + 6 Label Vertex axis of symmetry and two other points.
 * Practice:**

<span style="background-color: #000000; color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Section 2: Solving Quadratic Equations by Factoring
<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;"> <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">
 * Vocabulary**
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">__Monomial__: expression that has one term
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">__Binomials__: expression that has two terms
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">__Trinomial__: expression that has three terms
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">__Factoring__: processed used to separate trinomials as a product of binomials
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">__Zeros__: The numbers //p// and //q// are called zeros in the equation //y=a(x-p)(x-q)// ; //x = p// and //x = q//
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">media type="youtube" key="G_GBwuYuOOs" height="344" width="425"

<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">**Factoring Trinomials To factor //x//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">² + bx + c // ** <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">// To factor <span style="color: #000000; font-family: arial,helvetica,sans-serif;"> ////ax////<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;"> ² + bx + c// <span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;"> // **<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Factoring Patterns ** //
 * 1) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">Find integers //m// and //n//
 * 2) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;"><span style="color: #000000; font-family: arial,helvetica,sans-serif; line-height: 19px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">x //<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">² + bx + c = (x + m)(x + n) = ( //  <span style="color: #000000; font-family: arial,helvetica,sans-serif;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">x //<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">² + mx) + (nx + mn) //
 * 3) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">The sum of //m// and //n// must equal //b//, and the product of //m// and n must equal //c//
 * 1) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">Find integers //k// and //l,// as well as //m// and //nmedia type="custom" key="4873701" align="right" width="87" height="82"//
 * 2) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;"><span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 19px;">//ax//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">² + bx + c = (kx + m)(lx+n) = (klx //  <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">//² + kn) + (lmx + mn)//
 * 3) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive; line-height: 16px;">//k// and //l// must be factors of //a,// and //m// and //n// must be factors of //c//
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;"> Difference of Two Squares: //a////² - b² = (a +b)(a - b)//
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Perfect Square Trinomial: //a² + 2ab + b² = (a + b)²//

<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">**Zero Product Property** // **<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Finding Zeros ** //
 * <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">//ax//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">² + bx + c = 0 //
 * 1) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Change equation into Intercept Form
 * 2) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">Factor as usual
 * 3) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">When you reach, //(x ± # )(x ± #)//, replace x-value in each group with the value opposite of the # so that when added together they should equal zero
 * 4) <span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">The x-value in each grouping is the zero

<span style="color: #f07d0f; font-family: 'Comic Sans MS',cursive;">**Real Life Application** You can use quadratic equations in different jobs, such as finding appropriate dimensions for things like paintings, landmarks, etc.

Factor 3x^2 - 17x + 10
 * Practice:**

==<span style="background-color: #000000; color: #c6c624; font-family: 'Courier New',Courier,monospace;">Section 3: Solving Quadratic Equations by Finding Square Roots ==

<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">**Vocabulary**
 * <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">__Square Root__: a number //r// is a square root of a number //s//; //r//<span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;">//<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">² = s, √s = r // <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">
 * <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">__Radical Sign__: √
 * <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">__Radicand__: the number or expression beneath the radical sign
 * <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">__Radical__: the expression √//s// where //s// is a number
 * <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">__Rationalizing the Denominator__: process of eliminating a radical in the denominator of a fraction by multipling both the denominator and the numerator by denominator

<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">**Properties of Square Roots**
 * 1) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">Product Property:√//ab// = (√//a//)(√//b//)
 * 2) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">Quotient Property: √//a/b// = √//a/b//

<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">**Solving Quadratic Equations using Square Roots**
 * 1) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">Write original equation
 * 2) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">Get to the point where only the x <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">²-values are on one side and only a number is on the other side
 * 3) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">Take the square root of both sides
 * 4) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">Simplify
 * 5) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">Remember the answer will be both ±

<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">**Finding a Falling Object's Height using Quadratic Function**
 * 1) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">//h = -16t// <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">//²// //+ h₀//
 * 2) <span style="color: #c6c624; font-family: 'Courier New',Courier,monospace; line-height: 16px;">//h// is the feet; //t// is the seconds after the objects dropped; //h₀ is the initial height //

<span style="color: #c6c624; font-family: 'Courier New',Courier,monospace;">**Real Life Application** You can model real life quantities, such as the height of a rock dropped off the Leaning Tower of Pisa


 * Practice:**

Slove 2x^2 + 1 = 17

<span style="background-color: #000000; color: #008000; font-family: Georgia,serif;">Section 4: Complex Numbers
<span style="color: #008000; font-family: Georgia,serif;">**Vocabulary**
 * <span style="color: #008000; font-family: Georgia,serif;">__Imaginary Unit__: defined as //i//. //i// //= √-1//, //i// <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">² //= -1//
 * <span style="color: #008000; font-family: Georgia,serif;">__Complex Number__: //a// + //bi// where //a// and //b// are real numbers and //i// is the imaginary unit; //a// is always the real part of the complex number and //bi// is the imaginary part
 * <span style="color: #008000; font-family: Georgia,serif;">__Imaginary Number__: complex number //a// + //bi// where //b// ≄ 0
 * <span style="color: #008000; font-family: Georgia,serif;">__Complex Plane__: Coordinate plane where each point is (//a,b//) represents //a// + //bi//. Horizontal axis is for real numbers and vertical axis is for imaginary numbers.
 * <span style="color: #008000; font-family: Georgia,serif;">__Complex Conjugates__: Two complex numbers, //a// + //bi// and //a// - //bi//. The product is always a real number

<span style="color: #008000; font-family: Georgia,serif;">**Square Root of Negative Numbers** <span style="color: #333333; font-family: arial,helvetica,clean,sans-serif; line-height: 16px;"> // **<span style="color: #008000; font-family: Georgia,serif;">Solving a Quadratic Equation ** //
 * 1) <span style="color: #008000; font-family: Georgia,serif;">If //r// is a positive real number, then //√-r = i√r//
 * 2) <span style="color: #008000; font-family: Georgia,serif;">If r is a postive real number and follows the above, then (//i√r//) <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">² = -//r//
 * 1) <span style="color: #008000; font-family: Georgia,serif;">Write original equation
 * 2) <span style="color: #008000; font-family: Georgia,serif;">Get to the point where <span style="color: #008000; font-family: Georgia,serif; line-height: 19px;">only the //x// <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">²-values are on one side and only a number is on the other side
 * 3) <span style="color: #008000; font-family: Georgia,serif;">Take the square root of each side
 * 4) <span style="color: #008000; font-family: Georgia,serif;">Write in terms of //i// when taking the square root of a negative number
 * 5) <span style="color: #008000; font-family: Georgia,serif;">Simplify the radical
 * 6) <span style="color: #008000; font-family: Georgia,serif;">Remember the answer will be both ±

<span style="color: #008000; font-family: Georgia,serif;">**Plotting Complex Numbers**
 * 1) <span style="color: #008000; font-family: Georgia,serif;">The normal //x//-axis is now the Real Number axis, like wise the normal //y//-axis is now the Imaginary Number axis
 * 2) <span style="color: #008000; font-family: Georgia,serif;">Starting at the origin; the //a// value of the equation will follow the Real Number axis, the //b// value of the equation will follow the Imaginary Number Axis.

<span style="color: #008000; font-family: Georgia,serif;">**Multiplying Complex Numbers**
 * 1) <span style="color: #008000; font-family: Georgia,serif;">Use the Distributive Property or FOIL
 * 2) <span style="color: #008000; font-family: Georgia,serif;">Get all the number and values on to one side
 * 3) <span style="color: #008000; font-family: Georgia,serif;">Simplify and use //i// <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">² = -1
 * 4) <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">Answer should be in standard form; //a// <span style="color: #008000; font-family: Georgia,serif; line-height: 19px;">± //bi//

<span style="color: #008000; font-family: Georgia,serif;">// **Dividing Complex Numbers** //
 * 1) <span style="color: #008000; font-family: Georgia,serif;">Multiply the denominator and the numerator by the conjugate
 * 2) <span style="color: #008000; font-family: Georgia,serif;">Use FOIL
 * 3) <span style="color: #008000; font-family: Georgia,serif;">Simplify
 * 4) <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">Answer should be in standard form; //a// <span style="color: #008000; font-family: Georgia,serif; line-height: 19px;">± //bi//

<span style="color: #008000; font-family: Georgia,serif;">**Absolute Values of Complex Numbers**
 * <span style="color: #008000; font-family: Georgia,serif;">//|////z////| =// √//a// <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">² //+// <span style="color: #008000; font-family: Georgia,serif; line-height: 19px;">√//b// <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">²
 * <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">Used to find the number's distance from the origin in the complex plane
 * <span style="color: #008000; font-family: Georgia,serif; line-height: 16px;">When solving the //i//-value is disregarded

<span style="color: #008000; font-family: Georgia,serif;">**Real Life Application** You can use complex numbers to solve problems, such as determining whether a complex number belongs to the Mandelbrot set <span style="color: #008000; font-family: Georgia,serif;">**Practice:**

Slove 3x^2 + 10 = -26

<span style="color: #000080; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">**<span style="background-color: #000080; color: #ffffff; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 130%;">Section 5- Completing The Square **

//c = (b/2)²//
 * __Completing The Square__**: process that allows you to write an expression of the form //x² + bx// as the square binomial

1) set equation to //x² + bx = c// 2) add (b/2)² to both sides 3) factor into (x + b/2)² 4) square root both sides. 5) solve for x
 * Solving quadratic equation when coefficient of x² is 1 **:

<span style="color: #008000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">** Solving quadratics when coefficient of x² is not 1 ** <span style="color: #000080; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">: 1) divide each side by coefficient of x² 2) set equation to //x² + bx = c// 3) add (b/2)² to both sides 4) factor into (x + b/2)² 5) square root both sides 6) solve for x

Real Life Application- This is good for firefighters, because it can help them figure out where to position a fire hose where it would be most effective against the fire

Slove x^2 + 10x - 3 = 0 by completing the square
 * Practice:**

<span style="color: #800080; font-family: Tahoma,Geneva,sans-serif;">** Section 6- Quadratic Formula and Discriminant

__ Quadratic Formula __ **- x = -b ± <span style="color: #800080; font-family: arial,helvetica,sans-serif; line-height: 19px;">√b² <span style="color: #800080; font-family: Tahoma,Geneva,sans-serif;">- 4ac / 2a If: b² - 4ac > 0 ; 2 real solutions b² - 4ac < 0 ; 2 imaginary solutions b² - 4ac = 0 ; 1 real solution
 * __Discriminant__**- b² - 4ac

media type="custom" key="4882361"

media type="youtube" key="D_0vgqi7fU4" height="344" width="425" media type="youtube" key="dBtUetKJzOU" height="344" width="425" <span style="color: #800080; font-family: Tahoma,Geneva,sans-serif;">Real Life Application- This is good if you own an amusement park, because you can find the speed and duration of thrill rides by using the quadratic formula and the discriminant


 * Practice:**

Solve 2x + x = 5

** Section 7- Graphing and Solving Quadratic Inequalities **

<span style="color: #ff00ff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">__Quadratic inequalities with 2 variables__ <span style="background-color: #ffffff; color: #ff00ff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">: y>ax² + bx + c ; y__>__ax² + bx + c ; y<ax² + bx + c ; y__<__ax² + bx + c __**Quadratic inequalities with 1 variable**__: ax² + bx + c<0 ; ax² + bx + c__<__0 ; ax² + bx + c> 0 ; ax² + bx + c__>__ 0

1) Graph as you would a regular equation, remembering to use dashed or solid lines 2) pick a point and plug it in the equation to see if it's true or false. 3) shade on the appropriate side

Shade the region that makes the equation true. When shading: If shading the outside- OR statement (ex. x< -2 or x> 1) If shading inside- AND statement (ex. -2 < x <1) Real Life Application- You can solve real life problems like finding the weight of theater equipment that certain kinds of rope can support without breaking


 * Practice:**

Graph y > x^2 - 2x - 3 Label Vertex, Axis and two other points.

<span style="background-color: #000000; color: #808080; font-family: 'Times New Roman',Times,serif; font-size: 125%;">Section 8- Modeling with Quadratic Functions
 * __Quadratic__ ** <span style="color: #808080; font-family: 'Times New Roman',Times,serif; font-size: 94.5%;">: function <span style="color: #808080; font-family: 'Times New Roman',Times,serif; font-size: 105%;">that represents a real data set
 * __Vertex Form__**: //y = a(x-h)² + k//
 * __Intercept Form__**: //y = a(x-p)(x-q)//

1) Take the vertex points and put it in the equation so it's y = a(x-__h__)² + __k__ 2) Substitute the given point for x and y 3) Solve for the value of a. 4) Write the equation
 * Taking the vertex & given point and putting it into an equation**:

Using intercepts to write an equation: 1) Put the intercepts into the equation 2) Substitute the given point for x and y 3) solve for a 4) write equation

Real Life Application- You can solve important problems like determining the effect of wind on a runner's performance <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 105%;">
 * Practice:**

Answers: Vertex: (2,-2) Axis: x=2 (3x – 2)(x – 5) 2 square roots of 2 and -2 square roots of 2 X = + or 2i square roots of 3 X = -5 + or – 2 square roots of 7 X = about 1.35 and x = about -1.85 Vertex: (1,4) Axis: x = 1 Other Points: (-1,0) and (3,0)