FORMULAS

Distance Formula

The distance between two point in the Cartesian Plane with coordinates A(x1,y1) and B(x2,y2) has the formula:

This formula is dervied from the Pythagorean Theorem.

Quadratic Formula

The quadratic formula is used when finding solutions of a quadratic equation of the form:

While you may use the Quadratic Formula to solve all quadratic equations of this form, it is generally used to find the solutions of equations that cannot be factored using simple methods.

The portion of the Quadratic Formula under the square root sign is called the discriminant. If this value is negative then there are no real roots to this equation, but rather two distinct complex roots.

If there is no number in front of the second degree term (a) or the first degree term (b) it is understood that these values are 1. In math we don't usually include the 1 when writing the term. For example, in the statement x = 9 we don't typically write 1x = 9 even though that is its actual value.

Also if a term doesn't appear in an equation that value is assumed to be zero (0). Take for instance the equation x - 9 = 0. In this case the value of a is 0, b is 1, and c is -9. Although this equation can be solved easily without using the Quadratic Formula this shows how a term can be missing in an equation. Notice also that when there is a negative term we use that when placing it in the Quadratic Equation when solving.

Finally, you will notice in the Quadratic Equation the symbol:

This is read as "plus and minus". This means there are two values, one using plus (+) in this place and another using minus (-) here.