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.x^2 + 6x - 4y + 1 = 0

Accepted Answer

By completing the square, write the given equation into standard form and identify the vertex focus and directs of the para also graph the para and rectangular coordinate systems where we have X squared plus 10, X minus 12 Y plus 13 equals zero. Our possible answers, we have three different graphs and none of the above now have to solve this. We first need to turn this into standard form. Since we have an X squared in our equation, our standard form will be X minus H squared equals four P multiplied by Y minus K. Let's go ahead and change it into this form. But first, with all the X is on the left side and everything else on the right side, you'll have X squared plus 10, X equals 12, Y minus 13. Now, we need to complete the square to change our X square plus to X into our standard form. Completing the square. Just means we take the term on the X divide it by two and square, it then add it to both sides. In other words, B divided by two squared will be added to both sides. RB is 10. So we have 10 divided by two squared, which is 25. Let's add it to both sides. We get X squared plus 10, X plus 25 equals 12, Y minus 13 plus 25 which simplifies to positive 12. I'll add a plus 25 here just to show that we can now simplify our trinomial on the left. This simplifies to X plus five square. On the right side, we can factor out a 12, 12 multiplied by Y plus one. This is a standard form of a Parabola. We can also solve for P now because four P will multiply or what four P is equals to our 12, which means P equals three, we will use this to find our direct tricks and focus in a second. Let's first find our vertex. Our vertex is given by the point HK which we notice our H is in the parentheses with our X. So we get negative fifth. Our K is in the parentheses with the Y which is negative one. Our focus since this is a vertically oriented para our focus was given by the point H K plus P negative five. Neither one plus three gives us the point. The 52 are directs will be the equation Y equals K minus P. What we get neither one minus three, which is negative four. Other words, direct Trix is Y equals negative four. We now have everything we need for our answer. We have a vertex focused in direct tricks in our equation in standard form, which if we look at all of our possible answers, the answer to our problem corresponds to answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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.x^2 + 6x - 4y + 1 = 0

Key Concepts

Completing the Square

Standard Form of a Parabola

Vertex, Focus, and Directrix

Watch next