# How to graph a parabola #x=(y^2) - 4y + 3#?

##### 2 Answers

You prepare a chart of

#### Explanation:

Note that

**Step 1. Prepare a chart.**

Try an interval from

**Step 2. Plot these points.**

**Step 3.** Add points to make the plot symmetrical.

We need some extra points on the top portion of the graph.

Let's extend our table to

Here's the extended portion of the table.

Add these extra points to the plot.

And we have our graph.

If the question is to ** sketch** the parabola, you plot the vertex and the

#### Explanation:

**Warning!** This is a long answer.

Note that

We are going to get a sideways parabola.

**Step 1. Define your variables.**

The **standard form** for the equation of this parabola is

So

**Step 2. Calculate and plot the vertex. **

The vertex of the curve is given by

Calculate the x-coordinate of the vertex.

So the vertex is at (

Plot your vertex point.

**Step 3. Find the direction of the opening. **

The parabola will be a sideways U opening either to the right (

Since the coefficient

**Step 4. (optional) Draw the parabola's axis of symmetry. **

A parabola's axis of symmetry is a line that runs through its middle and divides it in half.

For a quadratic of the form

For our parabola, the axis is the line #y = 2.

It's not part of the parabola itself, but lightly marking this line on your graph can help you see how the parabola curves symmetrically.

**Step 5. Calculate and plot the #x#-intercept.**

The

**Step 6. Calculate and plot any #y#-intercepts.**

The x-intercepts are at (

Add these points to the graph.

**Step 7. Add any extra points to the graph.**

The

Plot this point.

**Step 7. Draw a smooth parabola passing through all the points.**