In Exercises 35–42, find the vertex, focus, and directrix of each...

Question

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.

(y + 1)^2 = - 8x

Accepted Answer

Using the provided equation find the paras vertex focus and directs then graph the para but we have Y plus nine squared equals negative four X. I noticed we have three possible answers with graphs. And our final answer is none of these answers. Now to solve this, we need to use the standard form of a parabola. Since we had the form of Y squared, our standard form is Y minus K squared equals four P multiplied by X minus H. Just since we have a horizontally oriented parabola, we could then use this to find our vertex. Our vertex is the point HK we notice here our H is zero because it should be on the X but there's no H there, our K is negative nine which is with the Y RP. We can use are four P defect, we have four P equals are negative four, which is the number that multiplies our X. This makes RP negative one. So our vertex then as a result is the 0.0 negative nine, our focus then since this is horizontal will be H plus P A, we have zero plus negative one or just minus one negative nine, which is negative one negative nine. Our direct tricks is the line X equals H minus P. Our H is zero and we're subtracting negative one, we get X equals one. We now have our vertex, our focus and our directs. If we look at our possible answers, we determine the answer to our problem is graph C OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (y + 1)^2 = - 8x

Key Concepts

Parabola Definition

Vertex, Focus, and Directrix

Graphing Parabolas

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