In Exercises 43–48, convert each equation to standard form by com...

Question

In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.

y^2 - 2y + 12x - 35 = 0

Accepted Answer

By completing the square, write the given equation into the standard form and identify the vertex focus and direct tricks of the Parabola. Also graph the Parabola and the rectangular recorded system where we have Y squared minus six Y plus eight, X plus 41 equals zero. Now we notice here we have the form Y square. This is, we have a horizontally oriented parabola. The standard formed then will be Y minus K squared equals four P multiplied by X minus H. So we need to turn our equation into this form. Let's first keep everything with Y on the left side and move everything else to the right side. You look it Y squared minus six Y equals negative eight X minus 41. Now let's complete the square. We'll take the term that's multiplying our Y divide it by two and square it and add it to both sides. We have negative six divided by two squared which simplifies tonight. So we will add nine to both sides. We get Y squared minus six Y plus nine equals negative eight X minus 32. We can now factor our left side as why minus three square the right side, we can factor out a negative eight to get negative eight multiplied by X plus four. We can also find RP in our standard form by setting equals to the term thus multiplying our X. In other words, our negative eight, we get P equals negative two. Now we have our equation, we can find our vertex focus and metrics. Our vertex is the point HK what you notice the H is on X negative four. The K is with our Y which is just three. Our focus since this is a horizontally orange super is the point H plus PK, we have negative four plus negative two. Now K is three which we get negative 63. Our directs will be X equals H minus P like so our H is now four subtracting RP negative two which is negative two. We get X equals negative two as a result. We now have everything we need to graph to trick focus vertex and R equation and standard form. If we look at our possible answers, we noticed our answer turns out to be answer C OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. y^2 - 2y + 12x - 35 = 0