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Analytic geometry

Precalculus Functions Anecdotes

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Calculus
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Mathematics
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Analytic functions
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Precalculus Functions Anecdotes

1. Identity Function-This is the only function thats acts on every real number by leaving it alone 2. Square Root Function-Put any positive number into your calculator. Take the square root. Then take the square root again, and so on. Eventually you will always get 1. 3. Squaring Function-The graph of this function, called a parabola, had a reflection property that is useful in making flashlights and satellite dishes. 4. Cubing Function-The origin is called a ?point of inflection? for this curve because the graph changes the curvature at the point. 5. Reciprocal Function-This curve, called a hyperbola, also has a reflection property that is useful in satellite dishes. 6. Natural Log Function-This function increases very slowly. If the x-axis and y-axis

Analytical Geometry Study Guide

Subject: 
Trigonometry
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geometry
Algebraic geometry
Conic sections
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Hyperbola
Ellipse
Asymptote
Parabola
Polar coordinate system
Semi-major axis
Linear equation

Analytical Geometry Formulas and Equations: Midpoint Formula of P(x1, y1), P?(x2, y2): Distance Formula of P(x1, y1), P?(x2, y2): Slope-Intercept Form y = mx + b Point-Slope Form y2 - y1 = m(x2 - x1) General Form of a Line Ax + By + C = 0 Standard Form of a Line Ax + By = C *Slope of line is (?A/B) Slope of P(x1, y1), P?(x2, y2): *Slopes of parallel lines are equal *Slopes of perpendicular lines are opposite and reciprocal Directed Distance from line Ax+By+C=0 to point P(x1, y1) * The sign of the denominator is the same sign as ?B? in the line. *The directed distance will be positive if the point P is above the line, and negative if P is below the line. Directed Distance Between 2 Parallel Lines *The parallel lines are: Ax+By+C & Ax+By+C?

Analytical Geometry Study Guide

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Trigonometry
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geometry
Algebraic geometry
Conic sections
Analytic geometry
Curves
Celestial mechanics
Astrodynamics
Hyperbola
Ellipse
Semi-minor axis
Semi-major axis
Parabola

Analytical Geometry Final Review Courtesy of Your Friend: Daryll Mu?oz Formulas and Equations: Midpoint Formula of P(x1, y1), P?(x2, y2): Distance Formula of P(x1, y1), P?(x2, y2): Slope-Intercept Form y = mx + b Point-Slope Form y2 - y1 = m(x2 - x1) General Form of a Line Ax + By + C = 0 Standard Form of a Line Ax + By = C *Slope of line is (?A/B Slope of P(x1, y1), P?(x2, y2): *Slopes of parallel lines are equal *Slopes of perpendicular lines are opposite and reciprocal Directed Distance from line Ax+By+C=0 to point P(x1, y1) * The sign of the denominator is the same sign as ?B? in the line. *The directed distance will be positive if the point P is above the line, and negative if P is below the line. Directed Distance Between 2 Parallel Lines

Graphing Linear Equations

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Algebra
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education

GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ SCORE:?____/14 Part?1:?Identifying?slopes?and?y?intercepts Identify?the?slope?and?y?intercept?of?the?given?linear?equations 1.?? [y 2 ?4 2. y ? [? 4 ?2 3.? 0[ 0y 1 ?2 4.? y 3 2 [ ?1 5.? y [ 6.?? ?y 8 9 ?7 Part?2:?Graphing?Linear?Equations Graph?the?following?linear?equations 7.? ? [y 2 ?3 Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 8. [y 2 1 ?4 9.?? ?y [ Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 10.?? ? [y 2 3 ?1 Part?3:?True?or?False Circle?the?letter?T?is?the?statement?is?True?and?circle?the?letter?F?is?the?statement?is

Conics

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Trigonometry
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geometry
Algebraic geometry
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Birational geometry
Parabola
Hyperbola
Ellipse
focus
Pole and polar
Euclidean geometry
conics

Analytic geometry is roughly the same as plane geometry except that in analytic geometry, figures are studied in the context of the coordinate plane. Instead of focusing on the congruence of shapes like plane geometry, analytic geometry deals with the coordinates of shapes and formulas for their graphs in the coordinate plane. Much of analytic geometry focuses on the conics. A conic is a two-dimensional figure created by the intersection of a plane and a right circular cone. All conics can be written in terms of the following equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 . The four conics we'll explore in this text are parabolas, ellipses, circles, and hyperbolas.

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