How to graph a parabola #x=(y^2) - 4y + 3#?
You prepare a chart of
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
Warning! This is a long answer.
We are going to get a sideways parabola.
Step 1. Define your variables.
The standard form for the equation of this parabola is
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
Step 6. Calculate and plot any
The x-intercepts are at (
Add these points to the graph.
Step 7. Add any extra points to the graph.
Plot this point.
Step 7. Draw a smooth parabola passing through all the points.