What are the differences between the Distance Formula, the Midpoint Formula, the Slope Formula, and the Quadratic Formula?

Question

What is each formula used for? Just need brief explanations.

Answer 1

The Distance Formula is a variant of the Pythagorean Theorem used in geometry.

The Midpoint Formula finds the midpoint of the line segment joining points.

The Slope Formula finds the slope of the line segment joining points.

The Quadratic Formula is the solution of the quadratic equation.

Answer 2

If P₁ has coordinates (x₁, y₁) and P₂ has coordinates (x₂, y₂), then the distance between the two points is

 

given by [(x₁ - x₂)² + (y₁ - y₂)²]^½ or [(x₂ - x₁)² + (y₂ - y₁)²]^½

 

Using the same two points as above, the midpoint formula is

 

M = [(x₁ + x₂)/2], [(y₁ + y₂)/2]

 

If we wanted to find the slope of the line on which the two points lie, it would be given by:

 

m = (y₁ - y₂)/(x₁ - x₂) or (y₂ - y₁)/(x₂ - x₁)

 

Some quadratic equations can be easily factored, some cannot.  For those cases we use the Quadratic Formula:

 

If ax² + bx + c = 0

 

then x = [-b ± (b² - 4ac)^½]/2a

 

Notice that the Distance, Midpoint and Slope Formulas all refer to linear equations.  The quadratic formula, as the name implies, is used to find roots of an equation in which the variable x is squared.