Question

Identify the coordinates for the vertex for each absolute value function.
f(x)=2|x−4|+5

f(x)=−|x+3|

f(x)=1/2|x|−3

f(x)=3|x−1|−2

Answer 1

Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows the Pythagorean theorem. It was probably the first number known to be irrational.[citation needed]

As a good rational approximation for the square root of two, with a reasonably small denominator, the fraction 99/70 (≈ 1.4142857) is sometimes used.

The sequence A002193 in the OEIS consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: