Introduction to Quadratics

Quadratic Equation

​ Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

​DEFINITION OF QUADRATIC EQUATION

​ A second degree equation is called quadratic equation. The general form of quadratic equation is ax²+bx+c=0. In this equation x represents as variable, whereas a, b, and c are constants where a is not equal to zero. If the value of a is zero then the equation is linear coefficient. Hence, a is the quadratic coefficient, b is the linear coefficient, and c is the constant.

​ There are two kinds of quadratic equations: the complete and incomplete quadratic equations.

ax²+bx+c =0 is a complete quadratic equation.

ax²+c=0 }

ax²+bx=0 } are incomplete quadratic equations.

ax²=0 ​ }

Examples

​ Determine the values of a, b, and c in the following:

Guided Practice

​

Encircle the number if it shows a quadratic equation. Write it in standard form and determine the values of a, b, and c.

​LESSON CHECK

1. What is a quadratic equation?

2. State the difference between quadratic and linear equations.

3. In a quadratic equation, ax²+bx+c=0, why can a not be equal to zero?