In Exercises 31–34, find the vertex, focus, and directrix of each...

Question

In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).

(x + 1)^2 = - 4(y + 1)

Accepted Answer

Choose the correct option for the vertex, direct tris focus and graph of the Parabola where we have X plus nine squared equals negative 16 multiplied by Y plus three. Now, to solve this, we need to make use of the general form of a Parabola. This is going to be a vertical parabola. So we will take the form X minus H squared equals four A multiplied by Y minus K. You notice here inside our vertex which is the point H K which has H equals negative nine A equals negative three. Now we can find our focus to find our focus. We need to find the A in our function. We notice four, a multiplies Y minus K and negative 16 multiplies Y plus three. In our equation, you will then set four A equals to negative 16 minus A equals negative four are focused in, in a vertical problem. It's H A plus A as the point you will then have negative nine with negative three plus negative four or minus four. Give me a sna of nine, negative seven. Our directs will be the opposite direction of our focus. We will say Y equals K minus A. That would be Y equals negative three minus negative four which gives us one we have. Why goes one negative nine, negative seven for our focus and negative nine negative three for our vertex. This corresponds with answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). (x + 1)^2 = - 4(y + 1)