Graphing quadratic inequalities in two variables

Lesson: 1
16:55
Lesson: 2
8:44

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Graphing quadratic inequalities in two variables

Grab a pen and grid paper for this lesson. We will learn the tricks on 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(x-p)^2 + q

, Graphing parabolas for given quadratic functions, Solving quadratic inequalities,

Lessons

1.
Graphing Quadratic Inequalities of Parabolas Opening Up
Graph:
i) $y = \frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$
ii) $y \ge \frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$
iii) $y$ < $\frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$

2.
Graphing Quadratic Inequalities of Parabolas Opening Down
Graph:
i) $y = - {x^2} - 4x$
ii) $y$ > $- {x^2} - 4x$
iii) $y \le - {x^2} - 4x$

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