## Introduction to Quadratic Inequality Calculator

Quadratic Inequality Calculator is an online tool that helps you to **find the graph line values** from the inequality equation in few a seconds. Our tool computes to get different kinds of point values of x,y to sketch a graph by using these point values.

## What is Graphing Quadratic Inequalities?

Graphing Quadratic Inequalities is a method through which you evaluate the **line graph points of (x,y) values** to make a graph from a quadratic inequality equation.

This inequality quadratic equation is different from the usual quadratic equation because it does not equal zero but has greater than or less than sign for example x^{2}+3x+5=0 to x^{2}+3x+5>0 etc.

## Rule of Quadratic Inequalities:

After the evaluation of the inequality quadratic equation, the Quadratic Inequality Calculator gives the root values that are used to draw a graph but it has some **cases due to inequality sign** for both one or two variable quadratic equations.

### For One Variable Quadratic Equation

In one variable quadratic equation, two cases are generated as per the equality of the quadratic equation.

- If your equation is
**ax**then you get a positive point of x value and the graph lies above the x value. A graph may become a closed interval.^{2}+bx+c>0 - If your equation is ax
^{2}+bx+c<0 then you get the negative point of the x value and the graph lies below the x value. A graph may contain an open interval.

### For Two Variable Quadratic Equations:

Two variable quadratic equations, two cases are obtained as per the equality of quadratic equation.

**Case 1**

If the quadratic equation solution has a positive root then the Graphing quadratic inequalities calculator draws a **solid parabola graph**. If the solution is a negative root value, then it draws a dashparabola that does not have a solution so this situation generates case 2.

**Case 2**

After sketching the dash parabola, the Quadratic Inequality Calculator adds different values of **x to get the value of y**. If the given y value does not satisfy the inequality condition as 5<3 then the graph value lies outside the parabola otherwise it lies inside the parabola.

## Working Method of the Quadratic Inequalities Calculator

Quadratic inequality solver has the simplest working method that can be easily understood by everyone without any difficulty. In this calculator, you can find the solution of the quadratic equation of one variable (x,x) and two variables (x,y) that give a number of line points on the graph.

When you enter your quadratic equation of **one or two variables** in the quadratic inequality graph calculator, check the nature of the given equation first.

After checking the behavior of the function it starts calculating the calculation process where if the equation belongs to one variable as ax^{2}+bx+c>0 then it can be solved with the bits of help of quadratic formula or factorization method.

If the given quadratic equation belongs to two variables(x,y) like **y>a(x1) ^{2}+bx^{1}+c**, then the calculator gives you a solution that makes a parabola graph.

Two types of methods are used by quadratic inequality calculator to solve the quartic equation of one or two variables.

### Factorization Method

Factorization method is one of the common methods that is used by Graphing quadratic inequalities calculator to solve the quadratic equation.

You just simply **factorize the given equation** and given x values as (x+a)(x+b) is equal to zero and get the x value points. Then use the given x values and sketch a point on the number line to make the graph.

### Quadratic Formula

Quadratic equation formula is the easiest method to solve the quadratic equation in which quadratic inequality solver **adds a,b, and c values** and gets the two roots that may be real or imaginary. After that, you use these roots to draw points on a number point graph.

Quadratic equation inequality is also solved using these two methods and gives two root values. For more root values quadratic inequality graph calculator adds different values of x in the given equation to get the value of y roots for making a parabola graph.

## Solving Quadratic Inequalities - Example

An example of a graphing quadratic inequalities question with a solution is given to let you understand **solving the graphing inequalities manually** and you can also learn how to understand the results of Quadratic Inequality Calculator,

### Example 1:

Solve the quadratic inequality of:

$$ x^2 + 5x \ge -6 $$

**Solution:**

The given equation is,

$$ x^2 + 5x \ge -6 $$

Factorizing it,

$$ (x + 2)(x + 3) \ge 0 $$

$$ (x+2)(x+3) \;=\; 0 \rightarrow x + 2 \;=\; 0 $$

$$ \;=\; x \;=\; -2 \;and \; x + 3 \;=\; 0 \rightarrow x \;=\; -3 $$

### PASTE THE GRAPH HERE!

### Example 2:

Solve the quadratic inequality and form a graph:

$$ y \gt -x^2 + x + 6 $$

**Solution:**

Graph the polynomial:

$$ y \;=\; -x^2 + x + 6 $$

$$ y \;=\; -(x^2 - x - 6) \rightarrow y \;=\; -(x + 2)(x - 3) $$

Equating the above equation to zero. So the roots are,

$$ x \;=\; -2 \;and \; x \;=\; 3 $$

So the inequality is greater thus the graph would have a dashed line.

### PASTE THE GRAPH HERE!

(1,2) is not the solution of this equation.

### Example 3:

Solve quadratic inequalities:

$$ 3x^2 - x - 5 \gt 0 $$

**Solution:**

$$ x \;=\; \frac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(-5)}}{2(3)} $$

$$ x \;=\; \frac{1 \pm \sqrt{61}}{6} $$

So the solution is:

$$ x \le -1.14 \;or\; x \gt 1.47 $$

### PASTE THE GRAPH HERE!

## How to Calculate in Quadratic Inequality Calculator?

Quadratic inequalities calculator has a simple design that allows you to solve various types of quadratic equation problems instantly. For this you need to **follow our instructions** then you won't find difficulty during calculation. These steps are:

- Enter the coefficient a,b,c,d value in the input field
- Check your function before pressing the calculate button to the actual solution of your input value
- Click the “Calculate” button for the solving quadratic inequalities question.

Click the “Recalculate” button for more evaluation to solve the quadratic inequality. - You can use the load example to see the evaluation process of solving quadratic inequalities problem.

## Output from Quadratic Inequality Solver

Quadratic Inequality Calculator gives you a **solution to your input function** in less than a minute when you click on the calculate button. It may include as:

**In result box**

You get the solution of a polynomial inequality equation problem.

**Steps box**

Click on the steps option so that you get the given solution of the Graphing Quadratic Inequalities problem in a step-by-step method.

**Plot box**

It gives you the solution in the form of a graph that draws with the help of root values (that gets after solving quadratic equation).

## Advanatges of Quadratic Inequality Graph Calculator

Quadratic inequality solver is a wonderful tool for solving polynomial root values as this tool gives you multiple **advantages whenever you use** it for calculating various types of quadratic equation problems. These advantages are

**Trustworthy tool**

It is a trustworthy tool as it always provides you with accurate results of solving quadratic inequalities problems.

**Speedy tool**

It is a speedy tool that gives the solution of Graphing Quadratic Inequalities problems in a couple of seconds.

**Free tool**

Graphing Quadratic inequalities calculator is a free online tool, you can find it for evaluation to solve quadratic inequalities without paying any charges

**Verstillty**

Quadratic Inequality Calculator is used for practice to solve various kinds of examples with solution

**Simple layout**

It has a simple design anyone or even a beginner can easily use to solve quadratic inequalities of quadratic equations.