We can think of the absolute value of a number as its distance from 0. So, the absolute value of a, which is denoted by is always greater than 0. In this post, we are going to prove that for all real numbers a, |-a| = |a|. There are two possible cases: and $latex b […]

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# Algebra

## Derivation of the Equation of the Parabola

A circle is a locus of points whose distance from a fixed point is a constant. A parabola can also be described as a locus of points whose distance from a fixed point and a fixed line not passing through that point is a constant. An example of a parabola is shown below. In the figure […]

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## Logarithm Base Changing Formula Proof

In a logarithmic expression, it is possible to change base using algebraic manipulation. For example, we can change to . In this post, we are going to prove why it is possible to do such algebraic manipulation. The change of base above can be generalized as . Theorem . Proof If we let , then […]

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