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
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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:
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