Table of Contents
Quadratic Equation Formula
The quadratic equation formula is a mathematical equation that is used to solve problems involving quadratic equations. A quadratic equation is an equation that contains a square term. The quadratic equation formula can be used to solve for the values of the variables in a quadratic equation.
Quadratic Equation: Definition
A quadratic equation is an equation in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The solutions to a quadratic equation are the roots of the equation, which are the points where the equation is equal to zero.
Solving Quadratics by Formula
Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.
The quadratic formula is:
where a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant term.
Examples of the Quadratic Equations :
1. x2 + 5x + 6 = 0
2. x2 − 4x − 5 = 0
3. x2 + 3x − 10 = 0
4. x2 − 6x + 9 = 0
Solving Quadratics by Factoring
The Quadratic Formula
Solving Quadratics by Completing the Square
Solving Quadratics by Quadratic Formula
Solving Quadratics by graphing
Solving Quadratics by using the Quadratic Formula
1. Solve the equation by factoring.
x2 + 10x = -6
x2 + 10x = -6
x2 + 10x + 36 = 0
(x + 6) (x + 6) = 0
x = 6 or x = -6
2. Solve the equation by completing the square.
x2 – 9 = 0
x2 – 9 = 0
x2 = 9
x = 3 or x = -3
