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 + 3)^2 = 12(x + 1)

Accepted Answer

Using the provided equation. Find the paras vertex focus and directs then to graph the para but we have Y plus eight squared equals a multiplied by X plus six. And we have three possible answers with graphs. And our final answer is just none of them. Now to solve this, we need to use the standard form of a parabola which is given by why minus K word equals four P multiplied by X minus H or a horizontally oriented pre. This is horizontally oriented because we have Y squared. Now let's found her HK and RP our H is with the X. We notice here we have a six, our H will then be negative six because their sin is positive. Similarly RK is negative A. Now the fine P we can say four P is equals to the number multiplying our X which is eight, dividing by four, gives us P equals two. Now we can find our vertex. First, our vertex is the point HK which in our case is negative six, negative eight. Our focus since this is horizontally oriented is going to be the point H plus PK or we have negative six plus two and negative eights which goes to negative four, negative eights. Our directs is the line X equals H minus P. We get negative six minus RP two which gives us negative eight. We get X equals negative eight. As a result are directs in focus and vertex will all help us graph our para if we look at our possible answers, we determine the answer to our question. His answer A with its corresponding graph. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y + 3)^2 = 12(x + 1)

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