A List of Lessons in the Quadratic Equations Curriculum
What Is a Quadratic Equation?
A quadratic equation is an equation in the form:
a, b and c are constants that stand in for particular numbers. x is a variable and can take any number. The highest power of x in a quadratic equation is 2. It has an x2 term.
Here is an example of a quadratic equation:
A quadratic equation shows a curve when plotted on a graph. Here is the quadratic equation above plotted on a graph:
Dictionary Definition
The Oxford English Dictionary defines a quadratic equation as "an equation of the second degree; specifically an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and x is unknown."Where Does the Word Quadratic Come From?
The word "quadratic" comes from the word "quad", meaning "square" - because the x is squared.Quadratic Equation Curriculum
All the lessons on this page are related to quadratic equations. They are grouped into mini-curriculums (or curricula if you prefer the Latin plural) to help you organise your learning. A brief description is given for each mini-curriculum. Click the MORE button for an overview of the topic and for the links to the specific lessons and tests.We Have Widgets!
Many of our lessons feature widgets like the one below. This widget lets you create your own graph and download it as an image, which – if you're a tutor – you might find useful for creating worksheets.Quadratic Equations
Quadratic equations are equations where x2 is the highest power of x. Quadratic equations show curves when plotted. In this mini-curriculum, you will learn about quadratic equations.
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Quadratic Equation
A quadratic equation is an equation in the form:
Quadratic equations show a curve when they are plotted on a graph:
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quadratic equations
Solving Quadratic Equations
Solving a quadratic equation means finding the value of x that make the equation equal to 0. There are different ways to solve quadratic equations. In this mini-curriculum, you will learn how to solve quadratic equations.
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Solve a Quadratic Equation
To solve a quadratic equation, find the value of x that makes the equation equal to 0:
Solve a Quadratic Equation Using Factoring
To solve a quadratic equation using factoring:
(1) Factor the Equation
Write the equation as two brackets multiplying each other.
Here is an example of factoring a quadratic equation into two brackets multiplying each other:
x2 + 5x + 4 = 0
⇒ (x + 1)(x + 4) = 0
(2) Solve the Equation
Equate each bracket to 0 to find the two values of x that solve the equation.
Here is an example of equating each bracket to solve the equation:
(x + 1)(x + 4) = 0
x + 1 = 0 ⇒ x = −1
x + 4 = 0 ⇒ x = −4
Solve a Quadratic Equation Using Factoring Where Leading Coefficient Is Not 1
A quadratic equation where there is a number before the x2 can be solved using factoring.
Here is an example of factoring and solving a quadratic equation where the leading coefficient is not 1:
(1) Factor the Equation
2x2 + 7x + 6 = 0
⇒ (x + 2)(2x + 3) = 0
(2) Solve the Equation
x + 2 = 0 ⇒ x = −2
2x + 3 = 0 ⇒ x = −3⁄2
Solve a Quadratic Equation Using the Quadratic Formula
To solve a quadratic equation using the quadratic formula, compare the quadratic equation with ax2 + bx + c = 0 to find the values of a, b and c. Substitute these values into the formula:
Solve a Quadratic Equation Using a Graph
To solve a quadratic equation using a graph, plot the quadratic equation on a graph and see where it crosses the x-axis.
Here is an example of a quadratic equation plotted on a graph. It is solved by x = 1 and x = 2:
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how to solve quadratic equations
how to solve quadratic equations using factoring
how to solve quadratic equations using factoring (where a ≠ 1)
how to solve quadratic equations using the quadratic formula
how to solve quadratic equations using a graph
Difference of Squares
A difference of squares is one squared quantity (a number or letter multiplied by itself) subtracted from another squared quantity. Some quadratic equations are in the form of a difference of squares. They can be factored and solved in an easy way. In this mini-curriculum, you will learn about the difference of squares.
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Difference of Squares
A difference of squares is square number (a number multiplied by itself) subtracted from another square number.
Here is an example of a difference of squares:
One square number (22 = 2 × 2) is being subtracted from another square number (32 = 3 × 3).
Solve a Quadratic Equation Using a Difference of Squares
To solve a quadratic equation using a difference of squares, factor and solve the quadratic equation.
(1) Factor the Equation
Write the equation as two brackets multiplying each other.
Here is an example of factoring a quadratic equation into two brackets multiplying each other using a difference of squares:
x2 − 9 = 0
⇒ (x + 3)(x − 3) = 0
(2) Solve the Equation
Equate each bracket to 0 to find the two values of x that solve the equation.
Here is an example of equating each bracket to solve the equation:
(x + 3)(x − 3) = 0
x + 3 = 0 ⇒ x = −3
x − 3 = 0 ⇒ x = 3
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a difference of squares
how to solve quadratic equations using a difference of squares
Completing the Square
Completing the square is a way of writing a quadratic equation. In this mini-curriculum, you will learn about completing the square.
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Perfect Square Trinomials
A perfect square trinomial is the result of squaring a binomial (two terms added or subtracted together).
Here is an example of a perfect square trinomial:
Completing the Square
Completing the square uses a perfect square trinomial to rewrite quadratic equations.
It is called completing the square because the method can be visualised as a square.
Complete the Square
To complete the square on a quadratic equation, write it as a squared binomial plus (or minus) a number.
Here is an example of completing the square on a quadratic equation:
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perfect square trinomials
completing the square
how to complete the square
This page was written by Stephen Clarke.
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