Chapter+10


 * || ............................................. Chapter 10 Vocab ||
 * __**Word**__ || **__Definition__** ||
 * Parabola || The graph of a quadratic function ||
 * Minimum Point || The lowest point of a parabola that opens up ||
 * Maximum Point || The Highest point of a parabola that opens down ||
 * Vertex || The maximum or minimum point of a parabola ||
 * Symmetry || A geometric property of figures that can be folded and each half matches the other exactly ||
 * Axis of Symmetry || The verticle line containing the vertex of a parabola, each point that is on one side of the axis of symmetry has a corresponding point on the parabola on the other side of the axis ||
 * Common Ratio || Ratio of a term to a previous term ||
 * Completing the square || Moving the terms to one side of the equation to make it square ||
 * Compound Interest || interest is earned on the interest and not just on original balance ||
 * Discriminant || The discriminant reveals what type of roots the equation has ||
 * Exponential Decay || a decrease that follows an exponential function. ||
 * Exponential Function || A function whose value is a constant raised to the power of the argument ||
 * Exponential Growth || Growth whose rate becomes ever more rapid in proportion to the growing total number or size ||

= 10-1 =


 * Graph quadratic functions.
 * Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola.

__You Need To...__
 * Create a table
 * Plot points
 * Connect the dots!

Rules: highest degree of a quadratic is always going to be 2 All exponents have to be positive

-If the value is negative the vertex is maximum value (opens down) -If the value is positive the vertex is minimum value (opens up)

1. Write the equation 2. Find axis of symmetry 3. Plug into equation: ax^2 - bx + c 4. Find y value for axis of symmetry 5. Make a table 6. Plot points 7. Connect the dots
 * Steps: **

= 10-2 =
 * Solve quadratic equations by graphing
 * Estimate solutions of quadratic equations by graphing

__1 Root__
 * Vertex
 * Axis of Symmetry
 * x-intercept

__Steps:__ 1. Write the equation 2. Find axis of symmetry 3. Put into equation: ax^2 - bx + c 4. Find the y value for axis of symmetry 5. Make a table 6. Plot the points 7. Connect the dots 8. The roots of the parabola are where the parabola crosses the x-axis (If exact roots can’t be found state the consecutive integers between which the roots lie.)

__**Real Life Parabolas**__
 * McDonlalds Arch || Roller Coaster || Slinkey || Football || Angry Birds ||
 * [[image:http://t3.gstatic.com/images?q=tbn:ANd9GcTBlL1NLFN-6Rf1Kdn8J8uHwS6Q-0D4fp1IGX9TGAsF1lBCH8WgNzI0qG3g width="102" height="79"]] || [[image:http://t2.gstatic.com/images?q=tbn:ANd9GcSh3DSYP-bc79gBUyaWEW5NMOxTYms2Yn_D8uZoloEhQD_hT4ZEaCB7A9uYMQ width="118" height="106"]] || [[image:http://t0.gstatic.com/images?q=tbn:ANd9GcSYaAyTH_aejq_J88HkY-6btf6DdRrtg0RHKx9AGJqxipfqY6ezfZF9_OiN0A width="124" height="107"]] || [[image:http://img1.photographersdirect.com/img/21627/wm/pd1300388.jpg width="140" height="109"]] || [[image:http://mrmeyer.com/blog/wp-content/uploads/111003_3hi.png width="148" height="112"]] ||

= 10-3 = __**Perfect Square**__ x^2 + 4x + 4 = 9 (x + 2)(x + 2) = 9 (x + 2)^2 = 9 Square the root of both x + 2 = +/-3 x + 2 = 3 .... x + 2 = -3 {-5, 1}
 * Solve quadratic equations by finding the square root
 * Solve quadratic equations by completing the square

__Steps:__ 1. Write the original equation 2. Factor 3. Take the square root of each side 4. Solve for the variable (remember you will have a positive and a negative solution to the square root) 5. Write your solution set.

**__Non-Perfect Square__** x^2 + 6x + 3 = 10 x^2 + 6x = 7 x^2 + 6x + 9 = 16 (x + 3)(x + 3) = 16 Square the root of both x + 3 = +/-4 x + 3 = 4 .... x + 3 = -4 {-7, 1}

__Steps:__ 1. Write the original equation .... a. You can't factor so subtract the constant (number) from both sides to get ax^2 + bx  .... b. Simplify .... c. Find a number that you can add to both sides by using the equation (b/2)^2 .... d. Add this number to each side .... e. Simplify 2. Factor 3. Take the square root of each side 4. Solve for the variable (you will have a positive and a negative solution because of the square root) 5. Write your solution set.

= 10-4 =
 * Solve quadratic equations by using the quadratic formula
 * Use the discriminant to determine the number of solutions for a quadratic equation.



.................................................................................. Will work for every single problem :)

//**Cannot get a square root of a negative number!**// __Steps:__ 1. Plug in a, b, c to quadratic formula 2. Simplify 3. Find solution set

= 10-5 =

y = 3^x **<** **exponent is the variable!**
 * Graph exponential function
 * Identify data that displays exponential behavior

Make a table to find the variable exponent- __X ....... Y__ 0 ....... 1 1 ....... 3  2 ....... 9  3 ...... 27

÷ /x exponential function +/- no exponential behavior

= 10-6 =
 * Solve problems involving exponential growth
 * Solve problems involving exponential decay

__**Growth -**__ y = c(1 + r)^t **y -** final amount **c -** initial amount **r -** rate of change (decimal) **t -** time (years)

__**Decay -**__ y = c(1 - r)^t **y -** final amount **c -** initial amount **r -** rate of change (decimal) **t -** time (years)

__**Compound Interest -**__ a = p(1 + r/n)^nt **a -** balance **p -** initial amount (principal) **r -** annual rate (decimal) **n -** number of times compounded per year **t -** time (years)

Formula **-** a//n// = a//1// * r^(n - 1)

10-7
 * Recognize and extend geometric sequences
 * Find geometric means