High School Algebra Archives - Page 12 of 31

Curve Sketching 2: Graphing Quadratic Functions

January 20, 2013 GB High School Algebra, High School Mathematics

In the first part of this series, we have learned 4 easy ways to graph linear functions. . In this post, we will learn how to sketch the graph of a quadratic function. Quadratic Functions are functions with equation $y = ax^2 + bx +c$ where $a \neq 0$ . This is the standard form. This equation can also be expressed in the form $y = a(x-h)^2 + k$ where $a \neq 0$ is the vertex form.

Unlike linear functions, we need more than two points to sketch the graph of quadratic functions. In the following discussion, we will examine the different properties of quadratic functions and use them to sketch their graph.

Here are some of the properties of $y = ax^2 + bx + c$ in relation to its graph. For students, it is really important that you think about them — don’t just memorize.

Graph Sketching I: 4 Easy Ways to Graph a Linear Function

January 19, 2013 GB High School Algebra, High School Mathematics

This is the first part of the Graph Sketching Series. Sketching is the process of drawing a rough idea of the overall shape of the graph. A graph sketch is a rough estimate of the actual graph of a function.

In this series, we will start with the graph of linear functions, then we will proceed with polynomial and rational functions later. We will also discuss how to sketch the graphs of trigonometric functions later.

In this post, we use different strategies to graph y = 2x – 1, a linear function. Since the graph of a linear function is a straight line, we only need two points to graph it. Here are four different ways to sketch the graph of linear functions. » Read more

2 comments curve sketching examples, graph sketching, graph sketching examples, graphing a linear function, sketching a linear function

4 Common Errors in Calculating Expressions with Exponents

December 20, 2012 GB High School Algebra, High School Mathematics

The errors below are usually made by students in calculating algebraic expressions with integer exponents. These errors result from the misunderstanding of the law of exponents.

If you have seen errors like the following, please don’t hesitate to use the comment box below.

Common Error 1 : $-a^n = (-a)^n$

That equation is only true if $n$ is odd. If $n$ is even, the equation does not hold. For example, in the expression $-3^4$ , the exponent $4$ only applies to $3$ and not $-3$ . That means that $-3^4 = - 81$ . However, $(-3)^4 = 81$ . » Read more

2 comments common errors in algebra, common errors in exponents, exponents calculation

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