About Second Degree Inequalities:

When we graph a non-linear inequality, we start with the boundary. We graph the boundary by replacing the inequality symbol with an equality symbol and graphing the resulting equation. We can use a test point to find and shade the appropriate region. When we encounter a system of non-linear inequalities, we graph each inequality and shade the overlap of the graphs as our solution to the system.


Test Objectives
  • Demonstrate the ability to graph the boundary of a non-linear inequality
  • Demonstrate the ability to graph a non-linear inequality
  • Demonstrate the ability to graph a system of non-linear inequalities
Second Degree Inequalities Practice Test:

#1:

Instructions: Graph each non-linear inequality.

a) $$y > x^2 - 3x$$


#2:

Instructions: Graph each non-linear inequality.

a) $$(x - 2)^2 + (y + 3)^2 < 4$$


#3:

Instructions: Graph each non-linear inequality.

a) $$\frac{(x - 1)^2}{1} + \frac{(y + 2)^2}{4} > 1$$


#4:

Instructions: Graph each non-linear system of inequalities.

a) $$y > -x^2 - 5x - 4$$ $$3x + 4y < 2$$


#5:

Instructions: Graph each non-linear system of inequalities.

a) $$x^2 + y^2 < 16$$ $$\frac{x^2}{4} - \frac{y^2}{25} ≥ 1$$


Written Solutions:

#1:

Solutions:

a)

the graph of a non-linear inequality: y > x^2 - 3x

#2:

Solutions:

a)

the graph of a non-linear inequality: (x-2)^2 + (y+3)^2 > 1

#3:

Solutions:

a)

the graph of a non-linear inequality: y > (x - 1)^2/1 + (y + 2)^2/4 > 1

#4:

Solutions:

a)

the graph of a system of non-linear inequalities: y > -x^2 - 5x - 4, 3x + 4y < 2

#5:

Solutions:

a)

the graph of a system of non-linear inequalities: x^2 + y^2 > 16, x^2/4 - y^2/25 > 1