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 - 2x - 4y + 9 =0

Accepted Answer

By completing the square, write the given equation into the standard form and then identify the vertex focus and direct tricks of the para also graph the para and a rectangular coordinate system. But we have X squared minus four, X minus four, Y plus 16 equals zero. We have four different answers here. Three with graphs and one which says none of these answers. Now to solve this, we first need to determine standard form of this problem. Since we have X squared, our standard form is X minus H squared equals four P multiplied by Y minus K. So we need to transform our equation into this form. We can do that by completing the square. Let's first move everything that is not an X to the right side, we will have X squared minus four, X equals four, Y minus 16. Now let's meet the square. We take the term that is on our X divide it by two, then square it and add it to both sets. Other words, we have a negative four. So we have negative four divided by two squared, which is four, you will add four to both sides as a result. We get X squared minus four, X plus four equals four, Y minus 12. We cannot factor the left side and the right side, the left side factors to X minus two squared. The right side will factor out four to get four multiplied by Y minus three. We can also find RP by taking the four multiplying our Y minus three and setting it equals to four P, our P is equal to one. Then we now have the equation of Standard form which means we can find our vertex focus and directs a vertex is given by the point HK which we can gather from our equation. The H is with our X which is two, the K is with our Y which is three. So our vertex happens at the 0.23 our focus since this is a vertically oriented para is given by the point HK plus P, we have 23 plus one, which is our point is 24. Our directors will be Y equals K minus P RK is three. RP is one, which means we get the line Y equals two. We now have our directs our focus, our direct tricks and our equation in Standard form. If we look at the possible answers, we can notice the answer to our problem. Turns out to be answer A 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 - 2x - 4y + 9 =0

Key Concepts

Completing the Square

Standard Form of a Parabola

Vertex, Focus, and Directrix

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