# Parabola Graph Calculator

Parabola Graph Calculator computes the graph for the given parabola equation. Parabola is defined as a locus of all points which are equally spaced from a fixed line and a fixed point. Parabola is obtained by slicing a cone parallel to the edge of the cone.

## What is Parabola Graph Calculator?

Parabola Graph Calculator is an online tool that helps to compute the graph for the given parabola equation. This online parabola graph calculator helps you to compute the graph in a few seconds. To use this parabola graph calculator, please enter the parabola equation in the given input box.

## How to Use Parabola Graph Calculator?

Please follow the steps below to compute the graph using an online parabola graph calculator:

**Step 1:**Go to Cuemath’s online parabola graph calculator.**Step 2:**Enter the parabola equation in the given input box of the parabola graph calculator.**Step 3:**Click on the**"Compute"**button to compute the graph for the given parabola equation.**Step 4:**Click on the**"Reset"**button to clear the field and enter a new parabola equation.

## How Parabola Graph Calculator Works?

**Parabola** is obtained by slicing a cone parallel to the edge of the cone. It is of U – shape as a stretched geometric plane. The general form of the parabola is given by y^{2} = 4ax

The general equation of a parabola is given by:

y = a(x - h)^{2} + k (regular)

x = a(y - k)^{2} + h (sideways)

Where (h,k) is the vertex of the parabola and a is the perpendicular distance from the focus to a point on the curve.

Let us understand this with the help of the following example.

**Solved Example on Parabola Graph**

Plot the parabola graph is given by the equation y^{2 }− 4y + 4x − 4 = 0 and verify it using the parabola graph calculator?

**Solution:**

The given equation can be rearranged as (y − 2)^{2 }= −4(x − 2)

This represents a parabola with vertex V(2, 2) and opening towards the left because a = –1 (negative).

The focus will lie at a distance of 1 unit to the left of (2, 2), i.e., at (1, 2)

The directrix will lie 1 unit to the right of (2, 2), i.e. it will be x = 3

Similarly, you can use the parabola graph calculator and compute for:

- y
^{2}= 15x - (y + 8)
^{2 }= −8(x + 5) - y
^{2 }− 10y + 6x + 9 = 0

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