Enable contrast version

TutorMe Blog

How To Find the Vertex of a Parabola

find vertex of parabola: Graph of a quadratic equation

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.

Read more

What Is the Pythagorean Theorem and When Is It Used?

What is the Pythagorean theorem: Graph of how the sum of the squares creates the right triangle ABC

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:

What is the Pythagorean theorem: a2+b2=c2 formula

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.

Read more

Here’s How Vector Subtraction Works

Graph showing the process of vector subtraction

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:

Formula for vector subtraction

Formula for vector subtraction

Formula for vector subtraction

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

Read more

Sine Function, Cosine Function, and Tangent Function Explained

Sine function in a right triangle

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 sine function: symbol θ. 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.

Read more

How To Find the Length of a Triangle

how to find the length of a triangle: Example of the Law of Sines in action

You’ll be asked how to find the length of a triangle over and over again in math and trigonometry. Maybe you need to find the missing side of a right triangle, maybe you know both side b and side c, or maybe you know only the opposite angle of the length of a side you are trying to find. In any case, we have formulas to help.

Read more
TutorMe homepage
Made in California by Zovio
© 2013 - 2021 TutorMe, LLC
High Contrast Mode
On
Off
BEST IN CLASS SINCE 2015