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Search Results for: Charlotte Taylor

How You Use the Triangular Proportionality Theorem Every Day

Diagram showing the triangle proportionality theorem

The triangle proportionality theorem is a geometric law stating that when you draw a line parallel to one side of a triangle, it’ll intersect the other two sides of the triangle and divide them proportionally. Regardless of whether they're obtuse, acute, or right triangles, this theorem can be used to determine unknown lengths within similar triangles.

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How To Master Quadratic Regression

quadratic regression graph

Similar to functions, quadratic regression is a way to model a relationship between two sets of independent variables. Quadratic regression is the process of determining the equation of a parabola that best fits a set of data. This set of data is a given set of graph points that make up the shape of a parabola. The equation of the parabola is y = ax2 + bx + c, where a can never equal zero.

The graphs of quadratic functions have a nonlinear “U”-shape with exponential curves on either side of a single intercepting y-value. We’ll show you how to use this equation.

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Three Types of Geometric Proofs You Need to Know

geometric proofs: Diagram showing a two column proof

Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. These steps are made up of reasons and statements.

There are many types of geometric proofs, including two-column proofs, paragraph proofs, and flowchart proofs. We’ll walk you through each type.

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One-to-One Functions: The Exceptional Geometry Rule

one-to-one function: Function F diagram

You need to understand one-to-one functions to grasp other concepts, like inverse functions. But first, let’s start with the definition of a function. A function is a geometric rule that shows a relationship between two sets of numbers. These ordered pairs of numbers are called the domain of the function (the input values) and the range of the function (the output values). In any given function, only one output value can be paired with a given input value.

See Function F below. This set of numbers is a function because no two outputs, or range values, have the same input, or domain values. However, it isn’t a one-to-one function. Let’s explore what this is.

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How To Use the Leading Coefficient Test To Graph End Behavior

leading coefficient test: leading coefficient is negative graph

You can use the leading coefficient test to figure out end behavior of the graph of a polynomial function. This isn’t some complicated theorem. There’s no factoring or x-intercepts. Here are two steps you need to know when graphing polynomials for their left and right end behavior.

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