## Introduction to Parabola Calculator:

Parabola Calculator is an online tool that helps you evaluate the given equation to **construct the parabola** on a graph. It uses the quadratic equation on a curve to find the line symmetry, vertex, x-intercept, or y-intercept for the parabola.

When you calculate the parabola problems by hand you consume much time because of its complex calculation or you may not achieve the desired result. In this situation, you need our parabola equation calculator which can solve the parabola equations for you.

## What is the Parabola?

A parabola is a quadratic equation on a curve that occupies **some points on a graph** in a U shape and each fixed point has an equidistant from a fixed line which is called the focus point and the fixed line is directrix.

It is an important concept in geometry to understand the properties of quadratic equations and physics to find the motion of projection and movement of satellites in statistical analysis. The equation of parabola behind the parabola calculator is:

$$ y \;=\; ax^2 + bx + c $$

## How to Calculate Parabola?

For the **calculation of the parabola** quadratic equation, the parabola graph calculator finds some important properties of the parabola like vertex, line-symmetric,y, and x-intercept values to construct a parabola shape on the graph.

Let's see how the parabola equation finder calculates the quadratic equation for a parabola on a curve in steps.

**Step 1**:

Identify the given equation y = ax^2 + bx + c where a, b, and c are constants.

**Step 2**:

To find the vertex form you need to find the x-coordinate vertex with the help of the given formula.

$$ x \;=\; -\frac{b}{2a} $$

For the value of y coordinate vertex put the x value in the given equation to get the vertex point.

**Step 3**:

The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two halves.so it has the same equation as the x-coordinate vertex has,

$$ x \;=\; -\frac{b}{2a} $$

**Step 4**:

Y-Intercept:

The point where the parabola intersects on the y-axis meets. To find the y-intercept put x = 0 as (0,c) in the given quadratic equation.

X-Intercepts:

These are the points where the parabola crosses the x-axis, and you can solve it by using the given quadratic equation in which put c = 0.

**Step 5**:

For the u shape graph of the parabola depends on different conditions which are:

- If a > 0, the parabola opens upwards on the graph.
- If a < 0, the parabola opens downwards on the graph.

## Practical Example of a Parabola:

The parabola calculator helps you to find equation of parabola easily but its important to understand the **calculation process** manually.

### Example: Find the Equation of this Parabola,

$$ y \;=\; -x^2 - 2x + 3 $$

**Solution**:

To determine the y-intercept put x = 0 to solve for y value,

$$ y \;=\;-x^2 - 2x + 3 $$

Put x = 0

$$ y \;=\; 0 - 2(0) + 3 $$

$$ y \;=\; 3 $$

The y-intercept is (0, 3). For the value of the x-intercept put y=0 in the given equation.

$$ y \;=\; -x^2 - 2x + 3 $$

Put y = 0,

$$ x^2 + 2x - 3 $$

Solve it,

$$ x^2 + 3x - x + 3 \;=\; 0 $$

$$ x(x+3) -1(x+3) \;=\; 0 $$

$$ (x+3)(x-1) \;=\; 0 $$

$$ (x+3) \;=\; 0,\; (x-1) \;=\; 0 $$

$$ x \;=\; -3,\; x \;=\; 1 $$

Here when y = 0, we obtain two solutions. There are two x-intercepts, (3, 0) and (1, 0)

To find the vertex value we use the equation for the line of symmetry,

$$ x \;=\; −\frac{b}{2a} $$

To find the x-value of the vertex.

$$ y \;=\; -x^2 - 2x + 3 $$

Here a = -1, b = -2, Put in the above equation

$$ x \;=\; -\frac{b}{2a} $$

$$ x \;=\; -\frac{(-2)}{2(-1)} $$

$$ x \;=\; -1 $$

Put x = -1 in the given equation to find the corresponding y value.

$$ y \;=\; -x^2 - 2x + 3 $$

$$ y \;=\; -1^2 - 2(-1) + 3 $$

$$ y \;=\; -1 + 2 + 3 $$

$$ y \;=\; 4 $$

The vertex is (−1, 4). For finding more point on a graph put x = 2 and y = 3,

$$ y \;=\; -(-2)^2 - 2(-2) + 3 \;=\; -4 + 4 + 3 \;=\; 3\; \; \; \; \; (-2,\; 3) $$

Now plot a graph using the vertex, y-intercept, x-intercept, or line-symmetric value to make a u-shaped parabola. As in the given equation a = -1 which is less than 0 the parabola falls downward.

$$ y \;=\; -x^2 - 2x + 3 $$

### PASTE THE GRAPH HERE!

## How to Use Parabola Calculator?

The parabola equation calculator has a simple interface that allows you to solve the parabola of a quadratic equation instantly. You just need to put your problem in it. Follow some instructions that help you to get the results of the parabola quadratic equation. These instructions are:

**Enter the given**parabola quadratic equation in the input box.- Review your given input equation value to get the exact solution of the parabola quadratic equation.
- Click the “Calculate” button for the evaluation of parabola quadratic equation problems.
- If you want to check the calculation of our parabola graph calculator then you can use the load example for its solution.
- Click the “Recalculate” button of the parabola finder for the evaluation of more examples of the parabola quadratic equation with the solution.

## Result from Parabola Equation Calculator:

Parabola Calculator provides you with a **solution** as per your input problem when you click on the calculate button. It may include as:

**In the Result Box**:

Click on the result button of the parabola equation finder so that you get the solution of the given parabola quadratic equation question.

**Steps Box**:

When you click on the steps option of the parabola formula calculator, you get the solution of the parabola equation questions in a step-by-step method.

**Plot Box**:

Plot box draw a sketch of a parabola on a graph that gives you an understanding of the parabola.

## Benefits of using Parabola Graph Calculator:

The parabola equation converter has different **benefits** whenever you use it to solve parabola quadratic equation problems to get the solution. Our tool only gets the input value and gives a solution of parabola without any trouble. These benefits are,

- The graphing parabolas calculator is a trustworthy tool as it always provides you with accurate solutions of the parabola quadratic equation.
- Our Calculator is a speedy tool that find equation of parabola with solutions in a few seconds.
- The parabola formula calculator is a learning tool that helps children about the concept of the parabola form of the equation very easily on online platforms at home.
- It is a handy tool that solves parabola equation problems quickly and you do not need to put any type of external effort.
- Parabola finder is a free tool that allows you to use it for the calculation of parabola equations without giving any fee.
- Parabola Calculator is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of parabola equation problems.