Quadratic Formula

Information (Quadratic Expressions, Equations and Functions)

The quadratic formula is one method that can be used to find the roots of quadratic equations of the form ax² + bx + c = 0.

Click here to see the derivation of the quadratic formula.

The radicand of the quadratic formula (b² - 4ac) is given the name "discriminant" and is represented by the symbol Δ.

The Quadratic Formula (using the discriminant)

Discriminant chart (a, b and c are Real numbers)

Discriminant chart (a, b and c are Rational numbers)

Example

Find the solutions to the quadratic equation: x² - 2x - 17 = 0 ( a = 1, b = -2, c = -17).

Solution to x<sup>2</sup> - 2x - 17 = 0 using the Quadratic Formula; Part 1

See how to re-write the entire radical (of 72) as a mixed radical.

Solution to x<sup>2</sup> - 2x - 17 = 0 using the Quadratic Formula; Part 2

Graphical Interpretation

Consider the graph of the quadratic function y = ax² + bx + c (and the specific example y = x² - 2x - 17).

Graph of Representative Sections of the Quadratic Formula

In the case of the specific example y = x² - 2x - 17, the axis of symmetry is x = 1. The x-intercepts are 3 root 2 left and right of the axis of symmetry.

Graph of Representative Sections of the Quadratic Formula for an Example

Demonstration

Image only

Instructions text as in global.js