How do you graph the inequality x^2 – 12x + 32 <12?

Mar 29, 2016

See the explanation

Explanation:

Given$\text{ } {x}^{2} - 12 x + 32 < 12$

Write as:

$\text{ } {x}^{2} - 12 x + 32 - 12 < y$

$y > {x}^{2} - 12 x + 20$

Now solve as a normal quadratic. Bulk a table of values and plot the curve. Remember that $y$ can not take on the actual curve value. It is stated as $y > \text{ and not as } y \ge$. The last one is the context in which $y$ could take on the value of the curve.

Or if you multiply everything by (-1) you get

$- y < - {x}^{2} + 12 x - 20$

Notice that this action turned > into < and that also $y$ became negative.$\textcolor{b r o w n}{\text{ However, both curves turn out to be the same.}}$