Gallery of Curves

$$y = ax + b$$ where $a$ is the slope, and
$b$ is the y-intercept.

$$x^2 + y^2 = r^2$$ Unit Circle: $$x^2 + y^2 = 1$$

$$(x+a)^2 + (y+b)^2 = r^2$$

$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

$$y = x²$$ A function with a second order nomial x² will have a parabolic shape,
concave if positive, convex if negative

Axis of symmetry.

$$y = \frac{1}{x}$$

Not to be confused with hyperbole, an exaggeration used as a figure of speech, like “it weighs a ton”.

Applications from wikipedia.
Path of sundial shadow.
Orbit of asteroid.

$$ y = \frac{1}{1+e^{x}}$$

y is always between 0 and 1.
s-shaped curve as in “sigmoid”.
asymptotes to 0 to the left and 1 to the right.

$$y = x² + 2ax + b$$

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• Scripts for these graphs are found in http://samantha.voyc.com/doc/script
• For more, see https://en.wikipedia.org/wiki/Gallery_of_curves.
• Khan Academy playlist: https://www.youtube.com/playlist?list=PLQPuPO-ipSuhNoqOUXasI1mAzSXubTv3z

Movement
Growth
Acceleration

cone
cone sliced by planes
conic section: circle, ellipse, parabola, hyperbola

equation of a plane
https://www.maplesoft.com/support/help/maple/view.aspx?path=MathApps%2FEquationofaPlane3Points

solving linear equations
3 planes in one cube
https://en.wikipedia.org/wiki/System//of//linear_equations
https://en.wikipedia.org/wiki/Linear_algebra

parametric equations
http://mathworld.wolfram.com/ParametricEquations.html

linear regression, multiple parameters
$$y = x₁w₁ + x₂w₂ + x₃w₃ + b$$