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### How to Graph a Circle

The first thing you need to know in order to graph the equation of a circle is where on a plane the center is located. The equation of a circle appears as [more…]

### How to Graph an Ellipse

An *ellipse* is a set of points on a plane, creating an oval, curved shape, such that the sum of the distances from any point on the curve to two fixed points [more…]

### How to Graph a Hyperbola

Think of a hyperbola as a mix of two parabolas — each one a perfect mirror image of the other, each opening away from one another. The vertices of these parabolas are a given distance apart, and they open [more…]

### How to Graph a Rational Function When the Numerator Has the Higher Degree

Rational functions where the numerator has the greater degree don’t actually have horizontal asymptotes. Instead, they have oblique asymptotes which you find by using long division. [more…]

### Distinguishing among Linear, Separable, and Exact Differential Equations

You can distinguish among linear, separable, and exact differential equations if you know what to look for. Keep in mind that you may need to reshuffle an equation to identify it. [more…]

### How to Use a Graphing Calculator

It’s a good idea to purchase a graphing calculator for pre-calculus work. Since the invention of the graphing calculator, math classes have begun to change their scope. A graphing calculator does so many [more…]

### How to Identify the Four Conic Sections in Graph Form

Each conic section has its own standard form of an equation with *x-* and *y-*variables that you can graph on the coordinate plane. You can write the equation of a conic section if you are given key points [more…]

### How to Identify the Four Conic Sections in Equation Form

Each conic section has its own standard form of an equation with *x-* and *y-*variables that you can graph on the coordinate plane. You can write the equation of a conic section if you are given key points [more…]

### 2 Ways to Graph a Circle

Circles are simple to work with in pre-calculus. A circle has one center, one radius, and a whole lot of points, but you follow slightly different steps, depending on whether you are graphing a circle [more…]

### How to Identify the Min and Max on Vertical Parabolas

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the *minimum* [more…]

### Calculus: How to Graph an Ellipse

An ellipse is basically a circle that has been squished either horizontally or vertically. From a pre-calculus perspective, an *ellipse* is a set of points on a plane, creating an oval, curved shape such [more…]

### How to Graph Conic Sections in Polar Form Based on Eccentricity

When you graph conic sections on the polar plane, you use equations that depend on a special value known as *eccentricity,* which describes the overall shape of a conic section. The value of a conic's eccentricity [more…]

### How to Change between Polar and Cartesian Coordinates

You can use both polar coordinates and Cartesian (*x, y*) coordinates (also known as rectangular coordinates) at any time to describe the same location on the coordinate plane. Sometimes you'll have an easier [more…]

### How to Find the Equation of Asymptotes

In pre-calculus, you may need to find the equation of asymptotes to help you sketch the curves of a hyperbola. Because hyperbolas are formed by a curve where the difference of the distances between two [more…]

### How to Graph a Hyperbola in 5 Steps

When graphing a hyperbola, you can think of it as a mix of two parabolas — each one a perfect mirror image of the other, and each opening away from one another. The mathematical definition of a hyperbola [more…]

### How to Graph Complex Numbers

To graph complex numbers, you simply combine the ideas of the real-number coordinate plane and the Gauss or Argand coordinate plane to create the complex coordinate plane. In other words, given a complex [more…]

### How to Plot Polar Coordinates

*Polar coordinates* are an extremely useful addition to your mathematics toolkit because they allow you to solve problems that would be extremely ugly if you were to rely on standard [more…]

### How to Graph Polar Coordinates with Negative Values

Sometimes your geometry teacher may spice things up a bit with *complicated polar coordinates* — points with negative angles and/or radii. The following list shows you how to plot in three situations — when [more…]

### How to Graph Conic Sections in Parametric Form

Sometimes your pre-calculus teacher may ask you to graph conics in parametric form. Parametric form is a fancy way of saying a form in which you can deal with conics that aren't easily expressed as the [more…]

### How to Graph a Vertical Parabola

In order to graph a parabola correctly, it is important to note whether it is a horizontal or a vertical parabola. This is because while the variables and constants in the equations for both curves serve [more…]

### How to Graph a Horizontal Parabola

A horizontal parabola features its own equations to find its parts; these are just a bit different when compared to a vertical parabola. The distance to the focus and directrix from the vertex in this [more…]

### How Graphs of Derivatives Differ from Graphs of Functions

When you start looking at graphs of derivatives, you can easily lapse into thinking of them as regular functions — but they're not. Fortunately, you can learn a lot about functions and their derivatives [more…]