Rate (mathematics)

In mathematics, a rate is a ratio between two measurements with different units. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity.

A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

An average rate can be calculated using the total distance travelled between a and b, divided by the travel time

An instantaneous rate can be determined by viewing a speedometer.

Minimum Point of a Quadratic Graph

Minimum Point of a Quadratic Graph

Differentiating the function and setting its derivative to 0 is the fastest way however if you do not know calculus then an alternate method is to complete the square. 

But for any quadratic in the form ax^2 + bx +c, where a, b and c are constants: the lowest point is when 

x = -b/2a.