Find an equation for the Parabola

Algebrator can help you find the equation for these Parabolas. Actually, it has specific Wizards that can help you.

Take a look at what I did to solve your problems using Algebrator.

First, I opened the "Equation of a Parabola using its Focus and Directrix" wizard. Note all the parabola-specific problems that Algebrator can solve.

Once the wizard was opened, I typed in the information provided by you:

the focus is (1, 0) and the equation of the directrix is x = -3, as shown in the image below.

TNext, I clicked the "Solve step" button in order to see the first step of the solution process. Since the step was quite "long", I decided to click on "Explain" in order to show you the explanation corresponding to that step. Take a look at the image below:

I clicked "Solve step" once more. Algebrator performed several (pretty simple) simplifications in one same step. Note that you can ask for an explanation for each of those simplifications, as shown in the image below:

Clicking "Solve step" several times more yields the final answer, as shown in the screenshot below. Note how The equations is written in its simplest form.

Note how the final step shows you the graph of the parabola together with its directrix and focus. The vertex is also drawn since it is a significant point.

Let's go on with the next part of the problem. In order to solve it, I selected the wizard "Equation of a parabola using its vertex and focus", as shown in the image below.

Just us I did in the first problem, here I also typed in the information provided by you in the input boxes that Algebrator shows.

I clicked "Solve step", and this is what Algebrator showed:

By looking at the previous image, you might ask yourself: but where did all those numbers come from?

The first step is definitely the crucial one in this kind of problems since it is the step where the entered information is substituted in the formulas. See how the explanation provided by Algebrator when you click on the "Explain" button helps you understand why each of the numbers that appear in the first step are there.

I went on clicking on "Solve step" and simplifications were done to the first equation. As the following screenshot shows, Algebrator shows you an explanation describing each of the simplifications performed.

If you go on clicking on "Solve step", Algebrator shows all the other simplification steps required to obtain the final equation of the parabola, which is highlighted in the image below:

The final step shows a graph of the parabola:

Finally, let's solve the third problem. Again, we select the most suitable wizard:

We enter the information provided:

And then we click "Solve step" to see the first step of the solution process:

The step is not so intuitive at first glance. That is why we ask for an explanation:

After several times of clicking on "Solve step", Algebrator reaches the final equation of the parabola.

The image below shows some of the simplification steps. Remember that you can tell Algebrator that you want to see more or less steps by changing the "Visibility" button.

Finally, Algebrator shows the graph of the given parabola, together with its vertex and the equation of its directrix.