In Exercises 5–16, find the focus and directrix of the parabola w...

Question

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.

y^2 - 6x = 0

Accepted Answer

For the following equation of a Parabola solve for the focus and directs and then graph Y squared minus 44 X equals zero. Now, to solve this, we will make use of the general form of a Parabola. The general form in our case should be Y minus K squared equals four. A multiplied by X minus H. Since we have a Y squared, we will have a horizontally oriented parabola facing either to the left or to the right. Let's rewrite our Parabola. In the standard form, we have Y squared minus 44 X equals zero. So let's move our X to the other side. You will get Y squared equals 44 X. Now we can find our A because we need the A to find our focus. We notice here four, a multiples our X and we have 44 that multiplies our X, let's say four A equals 44. And so for a, A will then be 11, we can then see our focus for a horizontally oriented parabola is H plus a comma K as a point where H K is our vertex, our vertex occurs as 00. In this case, So our focus will be zero plus 11 comma zero or 11 0. Now, our direct tricks is the opposite direction of our focus. We are adding A to find our focus. So we will subtract A to find our direct tricks. Or in other words, we will say X equals negative A, we then get X equals negative 11. Start focus being 11 0 tricks X equals negative 11. These both correspond two graph and B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. y^2 - 6x = 0

Key Concepts

Parabola Definition

Focus and Directrix

Graphing Parabolas

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