Solving Quadratic Equations by Factoring
A quadratic equation in which the quadratic trinomial has a leading coefficient of one can be solved by factoring. An example is given that also utilizes the zero factor property.
Solving Equations Not Written in Standard Form
Before solving a quadratic equation, it must be written in standard form. The procedure is demonstrated.
Quadratic Equations in Standard Form
The standard form for a quadratic equation is ax2 bx = 0. It is not always clear whether an equation is a quadratic equation until it is simplified. Any equation that can be written in stand form is a quadratic equation.
Quadratic Equations Can Have Two, One, or No Solutions
Quadratic equations with one variable can have one solution, two solutions, or no solution at all.
Parabola, The
Every parabola has an extreme value, which is the highest or lowest point on the curve, and is symmetrical.
Graphic of Quadratic Equations
All quadratic equations with two variables have an infinite number of solutions. When graphed, these ordered pairs lie on a curve called a parabola.
Practical Problem: Expanding a Parking Lot
Using a quadratic equation to solve a practical problem involving enlarging a parking lot. Checking the solution to be sure it makes sense in the context of the problem.
Practical Problem: The Path of a Golf Ball
Using a quadratic equation to describe the relationship between variables in a practical problem involving the flight time of a golf ball.
Solve: m2 7m 12 = 0
Practice solving a quadratic equation: m2 7m 12 = 0.
Examples of Quadratic Equations
Quadratic equations can have one or two variables, but in simplest form all quadratic equations have exactly one variable raised to the second power. Examples of quadratic equations are presented.