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# TutorMe Blog

## How To Find the Focus of a Parabola: Your Easy Guide

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Charlotte Taylor
February 17, 2021

If you want to know how to find the focus of a parabola, you first need to define what a parabola is. A parabola is a curved figure where any point on the curve is equal distance from a fixed point (called the focus) and a fixed straight line (called the directrix).

Let’s identify the parts of a parabolic function. In the graph above, you see a given line that intersects the directrix at a 90-degree angle. This straight line is called the axis of symmetry. The point that is marked C, signifying where the parabola opens, is called the vertex. The vertex is always midway between the focus and directrix of a parabola.

## Here’s How To Find the Hypotenuse of a Right Triangle

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Andrew Lee
February 08, 2021

The Pythagorean Theorem is an important theorem, as it comes up often in high school math. It makes the question of how to find the hypotenuse of a right triangle is easy to answer.

Plus, we can use it to find the base of a special right triangle and apply the converse of the Pythagorean Theorem. Let’s review this basic but foundational concept in trigonometry and how it relates to finding the hypotenuse of a right triangle.

## What To Remember When Graphing Linear Equations

Inactive
Andrew Lee
February 01, 2021

Graphing linear equations is key to helping you with making observations or insights about the equation. Before we look at graphing linear equations, let's review graphing basics.

The image above is a Cartesian graph. The x-axis goes left to right, and the x-intercept is wherever a straight line crosses over or intersects this horizontal axis. The y-axis goes up and down, and the y-intercept is wherever a straight line crosses over or intersects this vertical axis. Think of this as a rectangular coordinate system formed with evenly spaced perpendicular lines. Each ordered pair of coordinates (x,y) denotes a singular point on the graph.

The graph of a linear equation can be drawn by finding which x values and y values solve for the equation of the line, meaning those values balance the equation. For example, (2, 5) is a valid graph point for the equation , because substituting 2 for x and 5 for y in the equation gives 5 = 2(2)+1, or 5=5. (0, 0) is not a solution because 0≠0+1, or 0≠1, and therefore is not a point on the line. Once you have collected several points, you can graph your equation.

Find the x-coordinate of a point on the graph by counting the number of spaces along the x-axis in accordance with the first value. Then, find the y-coordinate by looking at the second number and counting that number of spaces up or down the y-axis. For example, the point (2,3) would be two spaces to the right and three spaces up.

## How To Find the Axis of Symmetry of a Parabola

Inactive
Andrew Lee
January 28, 2021

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

In this tutorial, we will show you how to find the axis of symmetry by looking at the quadratic equation itself.

## Understanding the Biconditional Statement

Inactive
Andrew Lee
January 28, 2021

A biconditional statement is a logic statement that includes the phrase, "if and only if," sometimes abbreviated as "iff." The logical biconditional comes in several different forms:

• p iff q
• p if and only if q
• p↔q

Consider the following statement: "You will read carefully on to the end of this article if and only if you are interested in reviewing converse statements, compound statements, and truth tables in order to understand what a true biconditional statement is."

Let's break it down.