Chapter+5

Welcome to the Chapter 5 page wiki!
 * __**Roles of Wiki**__ || __**Student #1**__ || **__Student #2__** ||
 * **Editor** || S. Pender ||  ||
 * **Multimedia** || B. Shoemaker ||  ||
 * **Text** || D. Overmiller ||  ||
 * **Practice Problems** || J. Scott ||  ||
 * **Career/Real Life App** || M. Sechrist ||  ||

5.1
 * __Quadratic function & Standard form-__** //y//=//ax// ²+//bx//+//c//
 * __Parabola-__** the graph of a quadratic function is U-Shaped
 * __Vertex-__** The lowest point on the graph of a quadratic function
 * __Axis of Symmetry-__** the vertical line through the vertex

5.2 Ex) //x//+3 Ex) //x// ² +8//x//+15
 * __Binomials-__** have two terms
 * __Trinomial-__** have three terms
 * __Factoring-__** Can be used to turn a Trinomal into a Binomial
 * __Monomial-__** an expression that has only one term
 * __Quadratic equation & standard form-__** ax ² +bx+c=0
 * __Zeros-__** The numbers //p// and //q// are called zeros in the equation //y//=//a//(//x//-//p//)(//x//-//q//)

5.3
 * __Square root-__** A number //r// is square root of a number //s// if //r// ² =//s//
 * __Radical sign-__** √
 * __Radicand-__** the number beneath the radical sign
 * __Radical-__** the expression √//s//
 * __Rationalizing the denominator-__** eliminating the square root in the denominator by multiplying both the numerator and the denominator by the denominator

5.4 __**Pure imaginary number-**__ If a=0 and //b// ≠0 __**Complex Plane-**__ every complex number corresponds to a point on this plane
 * __Imaginary Unit-__** //i// √-1 & //i// ²=-1
 * __Complex number & standard form-__** //a//+//bi//
 * __Imaginary Number-__** If //b// ≠0

5.5
 * __Completing the square-__** process that allows you to write an expression of the form //x// ²+//bx// as the square binomial

5.6 __**Quadratic formula**__ x = __-//b// ± __ __√//b//__ __²-4//ac//__ / 2//a// __**Discriminat-**__ //b// ²-4//ac//

5.7 __**Quadratic inequalities in two variables**__- //y////a//x// ² +b//x//+c, //y__>__//a//x// ² +b//x//+c,
 * __Quadratic inequalities in one variables__**- a//x// ² +b//x//+c<0, a//x// ² +b//x//+c__<__0, a//x// ² +b//x//+c>0, a//x// ² +b//x//+c__>__0,

5.8 __**Intercept Form**__- //y//=//a//(//x//-//p//)(//x//-//q//) __**Quadratic Model**__- a quadratic function that represents a real data set
 * __Vertex Form__**- //y//=//a//(//x//-//h//) ² +//k//

**An Intro to Quadratics** media type="custom" key="2722917"

**Solving Quadratic Equations by Factoring** media type="custom" key="2722927"

 **Completing the Square ABRA KADABRA!! This guy has fast (and neat) handwriting ** media type="custom" key="2722945"


 * __ 5.1 __**

Graph the quadratic equation.
** 1.) **** y = 2x ** ** 2 **** – 12x +19 ** ** 2.)  **** y = - (x-2) ** ** 2 **** - 1 ** ** 3.) **** y = 1/3 (x+4) (x+1) **  **1.)  ****q ** **<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">2 ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Times New Roman;"> – 7q –10 ** **<span style="color: rgb(51,153,102);">2.) ****<span style="font-size: 14pt; color: rgb(51,153,102);">9s ** **<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">2 ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Times New Roman;"> + 12s + 4 ** **<span style="color: rgb(51,153,102);">3.)  ****<span style="font-size: 14pt; color: rgb(51,153,102);">12y ** **<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">2 ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Times New Roman;"> – 25y –7 ** <span style="color: rgb(51,153,102);">1.) **<span style="font-size: 14pt; color: rgb(51,153,102);">5x ** **<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">2 ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Times New Roman;"> – 13x + 6 = 0 ** <span style="color: rgb(51,153,102);">2.)  **<span style="font-size: 14pt; color: rgb(51,153,102);">(w+6) ** **<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;"> 2 ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Times New Roman;">= 3(w+12) - w ****<span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">2 **<span style="font-size: 16pt; color: rgb(51,153,102); font-family: Times New Roman;">
 * You can check you answers in the back of you textbook on page SA16 (#21, 27, 35 on pages 253-254). ||
 * __<span style="font-size: 18pt; color: rgb(51,153,102); font-family: Times New Roman;">5.2 __**
 * <span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">Factor the expression. **
 * <span style="font-size: 14pt; color: rgb(51,153,102); font-family: Enviro;">Solve the equation. **
 * <span style="color: rgb(51,153,102); font-family: Times New Roman;">You can check you answers in the back of your text book on page SA16 (# 33, 51, 45, 67, 79) . ||

**__ 5.3 __**

<span style="color: rgb(255,0,255); font-family: Enviro;">Simplify the expression

 * 1.) [[image:http://www.purplemath.com/modules/radicals/rad17.gif width="18" height="17" align="bottom" caption="radical symbol"]] **** 2 ** ** 7 **** * [[image:http://www.purplemath.com/modules/radicals/rad17.gif width="18" height="17" align="bottom" caption="radical symbol"]] ** ** 7 **
 * 2.) [[image:http://www.purplemath.com/modules/radicals/rad17.gif width="18" height="17" align="bottom" caption="radical symbol"]] ** ** 75/36 **

<span style="color: rgb(255,0,255); font-family: Enviro;">Solve the Equation

 * 1.) 3x **** 2 **** = 108 **
 * 2.) **** 2 **** ( **** a-6) **** 2 **** – 45 = 53 **
 * <span style="color: rgb(255,0,255); font-family: Times New Roman;">Check Answers with the back of you textbook on page SA17 (#27, 41, 53, 65) ||

__<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Times New Roman;">5.4 __

**<span style="color: rgb(153,51,0);">Solve the equation **
<span style="color: rgb(255,117,0);">**<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">2<span style="color: rgb(185,90,34);">.)  <span style="color: rgb(185,90,34);">(-. 4 + . 9 i) - (-. 6 + i) 3.) (-4 + 2 i) (11 – 7) 4.) (15 - 8 i)<span style="font-size: 14pt; color: rgb(153,51,0); font-family: Enviro;"> 2 <span style="font-size: 16pt; color: rgb(153,51,0);"> <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">5.) __3 + __ __<span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';">i __<span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';"> 3 – i <span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';"> 6.) __6 - i____2__ 6 + i<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;"> 2 Find the absolute value of the complex number. <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">1.) 4 - 8 i **
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">3x ****<span style="font-size: 14pt; color: rgb(153,51,0); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;"> = -81 **
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">2.) ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">–1/8 (v +3) ****<span style="font-size: 14pt; color: rgb(153,51,0); font-family: Enviro;"> 2 ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;"> = 7 **
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">Plot the numbers on the same complex plane. **
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">4 + 2 ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';"> i **<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">Write the expression as a complex number in standard form. **
 * <span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">(2 + 3 ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';"> i ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">) + (7 + ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: 'Viner Hand ITC';">i ****<span style="font-size: 16pt; color: rgb(153,51,0); font-family: Enviro;">) **

<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Times New Roman;"> __<span style="font-size: 16pt; color: rgb(153,51,102);">5.5 __<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">Write the expression as the square of a binomial. 2.) **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">x ****<span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> - 4/9x + 4/81 **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> 2.)  **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">x ****<span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> + 84x + 300 =0 **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">
 * <span style="color: rgb(153,51,102); font-family: Times New Roman;">Check Answers with the back of you textbook on page SA18 (#25, 31, 49, 57, 73, 81) ||
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">1.) **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">x <span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> – 24x + 144
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">Solve the equation by completing the square **
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">1.) **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">x <span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> + 20x + 104 =0
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">Write the quadratic function in vertex form and Identify the vertex. **
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">y = x ****<span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> - 6x + 11 **
 * <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">2.) **<span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;">y = 3x <span style="font-size: 14pt; color: rgb(153,51,102); font-family: Enviro;">2 <span style="font-size: 16pt; color: rgb(153,51,102); font-family: Enviro;"> - 12x + 1

__<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Times New Roman;">5.6 __ <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">Use the quadratic formula to solve the equation. <span style="font-size: 18pt; color: rgb(51,204,204); font-family: Times New Roman;"> <span style="font-size: 200%; color: rgb(202,22,22); font-family: Verdana,Geneva,sans-serif;"> **__<span style="font-size: 18pt; color: rgb(51,204,204);">5.7 __**
 * <span style="color: rgb(153,51,102); font-family: Times New Roman;">Check Answers with the back of you textbook on page SA18 (#25, 31, 49, 57, 73, 81) ||
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">x ****<span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;"> - 5x – 14 =0 **
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">2.) 40x - 7x ****<span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;"> = 101 - 3x ****<span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 **<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">Solve using factoring, finding square roots, and quadratic terms. **
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">2.) ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">x ****<span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;"> - 5x – 14 =0 **
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">Find the discriminate of the quadratic equation and give the number and type of solutions of equation. **
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">1..) x ****<span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;"> + 3x – 6 = 0 **
 * <span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">3.) **<span style="font-size: 16pt; color: rgb(255,102,0); font-family: Enviro;">s <span style="font-size: 14pt; color: rgb(255,102,0); font-family: Enviro;">2 [[image:http://www.purplemath.com/modules/radicals/rad17.gif width="18" height="17" align="bottom" caption="radical symbol"]]5 + s + [[image:http://www.purplemath.com/modules/radicals/rad17.gif width="18" height="17" align="bottom" caption="radical symbol"]] 5 = 0
 * <span style="color: rgb(255,102,0); font-family: Times New Roman;">Check Answers with the back of you textbook on page SA18 (#17, 43, 49, 57, & 63) ||
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">Graph the system of inequalities. **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">1.) y > x ****<span style="font-size: 14pt; color: rgb(51,204,204); font-family: Enviro;">2 – ****<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">6x + 9 **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">2.) y < -x ****<span style="font-size: 14pt; color: rgb(51,204,204); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">+ 6x – 3 **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">Solve by graphing. **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">1.) ****<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">.3x ****<span style="font-size: 14pt; color: rgb(51,204,204); font-family: Enviro;">2 ****<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;"> + 24x __>__ -41 **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">Solve algebraically. **
 * <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">1.) **<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">2x <span style="font-size: 14pt; color: rgb(51,204,204); font-family: Enviro;">2 <span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;"> - 4x - 5 > 0
 * <span style="color: rgb(51,204,204); font-family: Times New Roman;">Check Answers with the back of you textbook on page SA18 (#31, 39, & 49) ||
 * __<span style="font-size: 18pt; color: rgb(51,51,0); font-family: Times New Roman;">5.8 __**
 * <span style="font-size: 16pt; color: rgb(51,51,0); font-family: Enviro;">Write the quadratic function in vertex form for the parabola. **

<span style="font-size: 16pt; color: rgb(51,51,0); font-family: Enviro;">**1.) whose points go through (0, 2) (4, 2) and a vertex of (2, -2)**

and a vertex of (-1, -6) **
 * <span style="font-size: 16pt; color: rgb(51,51,0); font-family: Enviro;">Write the quadratic function in intercept form for the parabola. **
 * <span style="font-size: 16pt; color: rgb(51,51,0); font-family: Enviro;">1.) Whose points go through (-2, 0) (1, 0)

<span style="color: rgb(0,0,0);">Write the quadratic function in standard form whose graph passes through the given points. <span style="font-weight: normal; color: rgb(51,51,0);"> 2.) (-6, 46) (2 , 14) (4 , 56) <span style="font-size: 16pt; color: rgb(51,51,0); font-family: Enviro;">
 * <span style="font-size: 14pt; color: rgb(51,51,0); font-family: Enviro;">1.) **(1, 2) (3 , 4 ) (6 , –5 )
 * Check Answers with the back of you textbook on page SA18 (#7, 17, 29, &33) ||

<span style="font-size: 16pt; color: rgb(51,204,204); font-family: Enviro;">

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">

<span style="display: block; color: rgb(219,53,15); font-family: Arial,Helvetica,sans-serif; text-align: center;">CAREER APPLICATION <span style="font-size: 150%; color: rgb(136,43,43); font-family: Arial,Helvetica,sans-serif;">Civil engineers design and build roads, bridges, buildings, and transit systems. Civil engineers use their knowledge of geometry, trigonometry and calculus to solve problems related to their work. Engineers, in general, apply mathematics and science to research, design, and develop a wide variety of products. This is often done by taking some scientific discovery and giving it a practical application. Engineers may also use their knowledge to improve existing things, such as the efficiency or quality of a product.

<span style="font-size: 18pt; color: rgb(51,204,204); font-family: Times New Roman;">