8.3 Graphing quadratic inequalities in two variables
In previous chapter, we were taught all about Quadratic Equations and Inequalities, which is why this lesson would just be a review of what we already know about inequalities. We know that inequalities are expression that has <, >, $\leq$ and $\geq$ in placed of the equality sign (=).
We also learned that inequalities can be in the form of linear inequality, quadratic inequality, and more. We were taught how to solve for them in the previous chapter. In this chapter we will focus on Inequalities with two variables.
In this chapter, we will have an introduction on inequalities, both linear and quadratic. While we already might have an idea as to what these two are, it’s still best to review them. In the first part of the chapter we will discuss a bit more on Linear Inequalities specifically on to graph them. In the second part of this chapter, we will learn how to graph systems of linear equalities. We will take a look at how to graph their solutions in a number line, how to graph solutions on an xy plane, and how to graph Linear inequalities with two variables.
For the third part of this chapter, we will look at the Quadratic Inequalities and to learn how to solve for the solution set. If you would recall, we already had a brief introduction on Quadratic Inequalities in previous chapter. We will review and take a look at their graphs and understand how to solve for the variables.
In the last part of this chapter we will learn how to graph a system of quadratic equation. We will also learn how to solve for any system of equation’s common ordered pair and how to algebraically and graphically show the boundary line between the expressions of an equation system.
Graphing quadratic inequalities in two variables
Basic concepts:
 Quadratic function in general form: y = $ax^2 + bx+c$
 Quadratic function in vertex form: $y = a(xp)^2 + q$
 Graphing parabolas for given quadratic functions
 Solving quadratic inequalities
Related concepts:
 Solving absolute value inequalities
Lessons

a)
$y = \frac{1}{3}{x^2}  \frac{2}{3}x  \frac{8}{3}$

b)
$y \ge \frac{1}{3}{x^2}  \frac{2}{3}x  \frac{8}{3}$

c)
$y$ < $\frac{1}{3}{x^2}  \frac{2}{3}x  \frac{8}{3}$


a)
$y =  {x^2}  4x$

b)
$y$ > $ {x^2}  4x$

c)
$y \le  {x^2}  4x$
