'2 4x' presentation slideshows

ANALYTICAL GEOMETRY

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Polynomials and Factoring

Polynomials and Factoring. The basic building blocks of algebraic expressions.

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Regents Review #3

Regents Review #3. Quadratics & More. Functions. Quadratic Functions. The graph of a quadratic function is a U-shaped curve called a parabola .

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6.1 Graphing Quadratic Functions

6.1 Graphing Quadratic Functions. Parabola Axis of symmetry Vertex. A Quadratic function. Parts of the Quadratic function. CONSTANT TERM. A Quadratic function. The graph of a Quadratic function is called a parabola. Parabola are Symmetrical. Axis of Symmetry, splits it down the middle.

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SECTION 4.2

SECTION 4.2. ONE-TO-ONE FUNCTIONS INVERSE FUNCTIONS. INVERSE FUNCTIONS. There are some functions which we almost intuitively know as inverses of each other: Cubing a number, taking the cube root of a number. Adding a value to a number, subtracting that value from the number.

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??????? ??. ??????? ?? y=ax 2 +bx+c(a?0) ??????. ? . ????????. ? . ???????. ? . ??????. ???????. y=ax 2 +bx+c (a<0). ???. y=ax 2 +bx+c (a>0). ????. ???. ??. ? a,b ? c ?????. ? a,b ? c ?????. ??. ??. ????. ??????? ,y ?? x ?????? . ??????? , y ?? x ??????.

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9.1 Conic Sections

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Multiplying and Factoring

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Functions and Graphs

Functions and Graphs. You should be able to sketch these graphs: y = x 2 and y = x 3. y = x 2. y = x 3. Functions and graphs. You should be able to sketch these graphs: y = and y = tan x. y = tan x. y = 1/x. Functions and graphs. You should be able to sketch these graphs:

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Math II

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???????. ????????. 1 ??????????. ? 1 ??????????. y=ax 2 +bx+c ? a?0 ?? ???????? a ??????? b ????? c ?. ???????? ? ?. ?????? x=-b/2a. ? 2 ??????????. y=a ? x+m ? 2 +k ? a?0 ?????????? -m ? k ?. 2 ??????. ?????? ? a>0 ?? ?????????? a<0 ???????????. 3 ?????.

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9.1 Parabolas

9.1 Parabolas. Parabolas. Notice that the axis of symmetry is the line through the focus, perpendicular to the directrix. Parabola: the set of points in a plane that are the same distance from a given point called the focus and a given line called the directrix. d 2. d 1. Focus. d 2.

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Warm Up

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5.8 Applications of Quadratic Equations

5.8 Applications of Quadratic Equations. Steps (reviews). Read and underline important words and numbers Assign variables Create equation and solve equation Check State answer. Problem with Geometric Figures.

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INTEGRATION & AREA

INTEGRATION & AREA. NB: we should think of a line as a very simple curve!. Consider. y = 2x + 3. Y. 8. B. Area(I) = 8 X 4 ? 2= 16. (I). A. Area(II) = 5 X 4 = 20. 4. Total = 36. (II). 5. X. 1 5. A is (1,5) & B is (5,13). Now consider. [ ]. 5. 5. ?.

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? ? ? ( ? )

? ? ? ( ? ). ????. ?????????????????????????? e ??????. (1) ? 0<e<1 ????. ? 2 ?? e>1 ??????. ? 3 ???? e=1 ??????? ?. y. y. y. y. F. K. 0. K. F. x. 0. 0. 0. x. x. x. F. K. K. F. ?????????? :. ??. y 2 =2px (p ? 0). ????. y 2 =-2px (p ? 0). x 2 =2py (p ? 0).

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D o Now:

D o Now:. Put your homework in the basket. What is the area of a rectangle? A triangle? Find the area of the rectangle whose length is (x + 3) and whose width is (2x + 5). Homework ?. Factoring Word Problems #1.

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X and y vary directly. If x = 4 and y = 12, then what will x be if y = 56? Is this a function?

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Linear Equations System In Three Variables

Linear Equations System In Three Variables. The Methods are used : elimination and substitution. Example :. 4x + y + 3z =10 5x +3y +7z = 13 6x -5y -2z = 2 Find the value of x + y - z. Given that. Solution :. Back to eq. 4 2x +z = 4 2(3) +z = 4 6 + z = 4 z = -2.

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