Substitution/Examples

Examples of Substitution

Arbitrary Example

Consider the expression:

$x^2 + 2 x + 6$

Substituting $2$ for $x$, we get:

$2^2 + 2 \times 2 + 6$

which evaluates to $14$.

This is called making the substitution $x = 2$.

If instead we making the substitution $x = y - 1$, the expression becomes:

$\paren {y - 1}^2 + 2 \paren {y - 1} + 6$

which simplifies to:

$y^2 + 5$

It is now easily seen that the expression cannot be less than $5$ in value, which happens when $y = 0$.

That is, when $x = -1$.