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Welcome to the Conic Sections course, Parabolas! Conic sections are the shapes that can be created when a plane intersects a double cone. The four types of conic sections are circles, ellipses, hyperbolas, and parabolas. In this course, we will be focusing on the conic section, the parabola.

Course Vocabulary
  • Open Downwards/Upwards – The direction the parabola opens up. A parabola that opens upwards looks like a smiley face, while a parabola that opens downwards looks like a frowny face.
  • Vertex (maximum or minimum point) – The highest or lowest point on a parabola.
  • Axis of Symmetry – The line throw the vertex that marks where the parabola is symmetrical.
  • Intercepts – Where the parabola crosses the x or y axis.
  • Slope – The change in y / change in x.
  • Secant line of a curve – Line that touches two or more points.
  • Value of a Limit – The value a function approaches as you get infinitesimally close to a specified point.
  • Infinity – a concept that is larger than any other number, and is used to discuss function behavior on the long term, infinity is not actually a number.
  • Infinitesimal – a concept that is closer to zero than any other number, and is used to discuss function behavior as close as possible to a specified value, also not actually a number.
  • Derivative Limit Definition – $ \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} $
  • Tangent – Line at a point which only crosses one point on the slope. This represents the rate of change at that point.
  • Multiplication by Constant – $\frac{d}{dx} (cf) = cf\prime$
  • Constant – $ \frac{d}{dx} (c) = 0 $
  • Addition – $ \frac{d}{dx}(f+g)=f\prime + g\prime $
  • Subtraction – $ \frac{d}{dx}(f-g)=f\prime – g\prime $
  • Power Rule – $ \frac{d}{dx}(x^n) = nx^{n-1} $
  • Product Rule – $ \frac{d}{dx} (fg)=f\prime g + fg\prime $
  • Quotient Rule – $ \frac{d}{dx} (f/g)=(f\prime g + fg\prime) / g^2$
  • Chain Rule – $ \frac{d}{dx}(f\circ g)(x)=f'(g(x))g'(x) $

While completing this course, chat with your friends through our disord link, or the chat/video features on our website. If you get stuck or just want to talk something through, you’ll probably find someone with the same question! Click the link below to visit our Discord channel for Parabola!