The quadratic inequality shows us in which interval the function is positive and in which it is negative - according to the inequality symbol. To solve quadratic inequalities correctly, it is convenient to remember two things:

Question Types:

The quadratic inequality shows us in which interval the function is positive and in which it is negative - according to the inequality symbol. To solve quadratic inequalities correctly, it is convenient to remember two things:

**Set of positivity and negativity of the function:**

Set of positivity - represents the $X$s in which the graph of the parabola is above the $X$ axis, with $Y$ value positive.

Set of negativity - represents the $X$s in which the graph of the parabola is below the $X$ axis, with $Y$ value negative.**Dividing by a negative term - reverses the sign of the inequality.**

- We will carry out the transposition of members and isolate the quadratic equation until one side equals 0. Remember that when we divide by a negative term, the inequality is reversed.
- Let's draw a diagram of the parabola - placing points of intersection with the $X$ axis and identifying the maximum and minimum of the parabola.
- Let's calculate the corresponding interval according to the exercise and the diagram.

Quadratic equation $>0∶$ Set of positivity

Quadratic equation $<0∶$ Set of negativity

Question 1

Solve the following equation:

\( x^2+4>0 \)

Question 2

Solve the following equation:

\( -x^2+2x>0 \)

Question 3

Solve the following equation:

\( -x^2-9>0 \)

Question 4

Solve the following equation:

\( x^2+9>0 \)

Question 5

Solve the following equation:

\( x^2-9<0 \)

Solve the following equation:

x^2+4>0

All values of $x$

Solve the following equation:

-x^2+2x>0

0 < x < 2

Solve the following equation:

-x^2-9>0

There is no solution.

Solve the following equation:

x^2+9>0

All values of $x$

Solve the following equation:

x^2-9<0

-3 < x < 3

Question 1

Solve the following equation:

\( -x^2+3x+4>0 \)

Question 2

Solve the following equation:

\( x^2-3x+4<0 \)

Question 3

Solve the following equation:

\( x^2-6x+8<0 \)

Question 4

Solve the following equation:

\( x^2+4>0 \)

Question 5

Solve the following equation:

\( x^2-8x+12>0 \)

Solve the following equation:

-x^2+3x+4>0

-1 < x < 4

Solve the following equation:

x^2-3x+4<0

There is no solution.

Solve the following equation:

x^2-6x+8<0

2 < x < 4

Solve the following equation:

x^2+4>0

All values of $x$

Solve the following equation:

x^2-8x+12>0

x < 2,6 < x

Question 1

Solve the following equation:

\( x^2+4x>0 \)

Question 2

Solve the following equation:

\( x^2+4x>0 \)

Question 3

Solve the following equation:

\( x^2-2x-8>0 \)

Question 4

Solve the following equation:

\( x^2-25<0 \)

Question 5

Solve the following equation:

\( -x^2-25<0 \)

Solve the following equation:

x^2+4x>0

x < -4,0 < x

Solve the following equation:

x^2+4x>0

x < -4,0 < x

Solve the following equation:

x^2-2x-8>0

Answers (a) and (c)

Solve the following equation:

x^2-25<0

-5 < x < 5

Solve the following equation:

-x^2-25<0

All values of $x$