# TutorMe Blog

## Test: Introverts Have The Potential To Learn More Effectively Via Online Tutoring

The pandemic thrust students and teachers into virtual learning with little time to prepare. Many teachers and students alike had to figure out how to adapt on the fly. Some students struggled to acclimate to online learning.

For many introverted students, however, online learning gave them new opportunities to thrive. Some students quickly discovered that online learning provided more opportunities to learn at their own pace, slightly separated from other students.

Online learning, in many cases, also offers more direct, one-on-one interaction with an instructor.

## How To Find the Vertex of a Parabola

To find the vertex of a parabola, you first need to know how to graph quadratic equations. When graphing these, remember that every quadratic function can be put into a standard form (more on this later). This allows you to find the leading coefficient and solve for the x-intercepts. The x-intercept and y-intercept are points on the graph where the parabola intersects the x-axis or y-axis.

Putting the quadratic function into standard form will also let you find the axis of symmetry, the line that runs through the vertex and divides the parabola in half. You can then find the x-coordinate and y-coordinate of the vertex, which is the highest or lowest point on a parabola.

## What Is the Pythagorean Theorem and When Is It Used?

What is the Pythagorean theorem? It’s a trigonometry equation used to find the length of one side of a right triangle. Though similar concepts had been discovered by the Babylonians, Greek Mathematician Pythagoras was the first person to come up with a geometric proof about how the sum of the squares of the lengths can determine the side lengths of a right triangle.

Pythagoras determined that when three squares are arranged so that they form a right angle triangle, the largest of the three squares must have the same area as the other two squares combined. In the picture below, you can see how the sum of the squares creates the right triangle ABC.

This realization about the area of the squares led to the Pythagoras theorem:

Squares are different from other parallelograms and trapezoids because all their sides are equal lengths. So since squares are made up of four equal sides, you can see that each individual square makes up a side of the right triangle.

The length of the largest square, which we'll call length c, is the length of the hypotenuse. (The hypotenuse is the longest side of a right triangle.) The smaller squares make up the other two sides of the right triangle.

## Here’s How Vector Subtraction Works

A vector is a term used to define any line segments with a specified starting and ending point. All vectors are drawn at an angle and have a specified direction. Learning to subtract vectors is helpful when you need to see how much one vector must travel to get to the other.

Vector subtraction is the process of subtracting the coordinates of one vector from the coordinates of a second vector.

See the example below. The coordinates of vector a are marked as (3,3) and the coordinates of vector b as (1, 2).

When subtracting vectors, you must take the first vector quantities and subtract the second quantity. Let's subtract vector b from vector a:

Your resultant vector coordinates for this particular example are (2, 1).

## Sine Function, Cosine Function, and Tangent Function Explained

There are three basic functions to understand in trigonometry: sine function, cosine function, and tangent function. Each function takes in an angle measure, which is called theta and represented by the symbol . The angle measure is usually expressed in radians or degrees. The output of the function is a ratio comparing one side of the triangle to another.