Curves

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human

Human population Out line .4.1 How population change over time A. B. C. D. II. Age structure A. B. C. D. E. F. G. H. I. J. K. 4.2 Kinds of population Growth III Exponential growth A B C IV A brief history of human population Growth 1. 2. 3. 4. 4.3 Present Human Population Rates of Growth A. B. C. D. E. F. 4.4 Project Future Population Growth A. V. Exponential Growth and daubing Time A. B. C. D. E. The logistic Growth Curve A. B C D E. F. G. VII. Forecasting Human Population Growth Using the logistic Curve A. B. C. D. E.

Function

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Y=X is a parent function as well as Y=X squared. However, the second function makes a parabola.

Function

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Y=X is a parent function as well as Y=X squared. However, the second function makes a parabola.

Parabola Notes

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To derive the focus of a simple parabola, where the axis of symmetry is parallel to the y-axis with the vertex is at (0,0), such as then there is a point (0,f) ? the focus, F ? such that any point P on the parabola will be equidistant from both the focus and the linea directrix, L. The linea directrix is a a line perpendicular to the axis of symmetry of the parabola (in this case parallel to the x axis) and passes through the point (0,-f). So any point P=(x,y) on the parabola will be equidistant both to (0,f) and (x,-f). FP, a line from the focus to a point on the parabola, has the same length as QP, a line drawn from that point on the parabola perpendicular to the linea directrix, intersecting at point Q.

Parabolas

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Film

Parabolas Graphs a parabola, showing coefficients for the equation in both standard form, y=a(x-h)2+k, and general form, y=ax2+bx+c. How to use || Examples || Other Notes -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- How to use To change the values of the coefficients, use the "+" and "-" buttons under each value. The buttons change the value by 0.1 at each step. Holding a button down causes this action to be repeated. Click the "Clear" button to reset all values to the default values, a=1 and all other values are 0. -------------------------------------------------------------------------------- Examples Horizontal shifts: in standard form,

Parabola

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Parabolas and their functions

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Parabolas 1.Normal Parabola f(x) = x? root : (0/0) apex : deepest point/highest point of the parabola 2.Displacement up/down the y-axis f(x) = x?+k root : 1 solution: k = 0 2 solutions: k > 0 0 soltuions: k < 0 apex : (0/k) 3.Displacement on the x-axis f(x) = (x + h)? root = apex : (-h/0) 4. Displacement on x- and y-axis f(x) = a(x+h)? + e root : look at 2. aspex : (-h/k)
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Unit circle

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Geometry

Circles

Conic sections

Spheres

Unit circle

Generalized trigonometry

Pi

N-sphere

In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, "the" unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

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Unit circle

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Geometry

Circles

Conic sections

Spheres

Unit circle

Generalized trigonometry

Pi

N-sphere