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Parabola

Physics Lab 6

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Adelinne Wenger Analyzing a Projectile?s Motion Lab #6 11/13/15 Mr. Glasel Period 5 Questions 1a. Plot a graphs of the following: Horizontal Position and Vertical Position vs. Time (on the same axis) Horizontal Velocity and Vertical Velocity vs Time (on the same axis) Horizontal Acceleration and Vertical Acceleration vs Time (on the same axis) Refer to data 1b. Describe the type of motion indicated by the horizontal motion graphs. The motion indicated by the horizontal motion graph in the first graph is a linear relationship; as time increases, the distance also increases. On the other two graphs, the velocity and acceleration stay the same as time passes making it a graph that isn?t linear.

Precalc conic review station activity

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Station 1: Write the equation for a circle with a diameter that has endpoints of (1, 5) and (12, -2). Station 2: Find an equation for the hyperbola with center at (1, -2) and vertices at (4, -2) and (-2, -2), with a conjugate axis of length 10. Station 3: Determine an equation for the parabola with focus (3, 6) and directrix y = -2. Station 4: Find the vertex, focus, directrix and focal width of the parabola with equation , then graph it. Station 5: Determine an equation for the parabola with vertex (2, 4) and focus (0, 4). Station 6: Determine the major and minor vertices, center, and foci of the ellipse , then graph it. Station 7: Determine what type of conic is, then identify all key information and graph it. Station 8:

alg2 review

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H/GT Algebra II - Semester Exam Final Review 1.) Solve 4 264 16 1 0b b? ? ? 2.) What is the vertex of 23 24 5y x x? ? ?? 3.) Graph 22( 1) 1y x? ? ? 4.) Solve 25 19 4n n? ? 5.) Write an equation of a parabola that passes through the points (0, 2), (-2, 6), and (6, 14). 6.) Write the equation for the graph below. 7.) Write an equation of a parabola (general form) with vertex (0, 0) and directrix y = 2. 8.) Find the vertex of 24 4x y y? ? 9.) Graph 2 3y x? ? 10.) Write an equation of a circle with center (4, -3) and radius 5. (General form) 11.) Find the center and radius: 2 2 8 4 12 0x y x y? ? ? ? ?

Analytical Geometry Study Guide

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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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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

Conics

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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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