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).

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

Accepted Answer

Choose the correct option for the vertex. Direct tricks focus and graph of the problem where we have Y minus nine squared equals negative 16 multiplied by X minus three. Our possible answers are three different graphs here and none of these graphs. Now to solve this, we will make use of the general form of a horizontally oriented parabola. This form is Y minus K squared equals four. A multiplied by X minus H. We can then first find our vertex, our vertex is the point H K. But if you know this, our H is three in our K is nine. Now we can find the focus to find the focus. You first need to find a, we notice we have four, a multiplying XX minus H. And in our function, we have negative 16 multiplying X minus three. We can then set four A equals to 16 which is negative that makes a equals to negative four. Now let's find the focus our focus in a horizontal parabola. It's H plus A com as a point our eight here is three R A is negative four and which drop down R K. We get negative one. Not our directs will be the opposite direction of our focus, which is X equals H minus A. We get X plus three minus negative four which gives X equals seven. We now have our vertex. We have our focus and we have our directions. If we look at our possible graphs, we have a parabola faces to the left which his answer is C 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). (y - 1)^2 = - 4(x - 1)