Graphing systems of quadratic inequalities - Inequalities in Two Variables

Graphing systems of quadratic inequalities

A system of inequalities means that there are more than two inequalities we need to look at to answer the questions. One way to solve this kind of questions is by graphing the systems of quadratic inequalities out.

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
System of quadratic-quadratic equations

Related concepts:
Solving absolute value inequalities

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Graphing systems of quadratic inequalities

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AlgebraQuadratic function in general form: y=ax2+bx+cy = ax^2 + bx+cy=ax​2​​+bx+c

AlgebraQuadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + qa(x−p)​2​​+q

AlgebraGraphing parabolas for given quadratic functions

AlgebraSystem of quadratic-quadratic equations

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Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+cy=ax​2​​+bx+c

Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + qa(x−p)​2​​+q

Graphing parabolas for given quadratic functions

System of quadratic-quadratic equations

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1.

Solve the system: yyy > 13x2−23x−83\frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}​3​​1​​x​2​​−​3​​2​​x−​3​​8​​ y≤−x2−4xy \le - {x^2} - 4xy≤−x​2​​−4x

Graphing systems of quadratic inequalities

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Quadratic function in general form: $y = ax^2 + bx+c$

Algebra
Quadratic function in vertex form: y = $a(x-p)^2 + q$

Algebra
Graphing parabolas for given quadratic functions

Algebra
System of quadratic-quadratic equations

Quadratic function in general form: $y = ax^2 + bx+c$

Quadratic function in vertex form: y = $a(x-p)^2 + q$

or

Solve the system:
$y$ > $\frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$
$y \le - {x^2} - 4x$