Question

The vertex of the parabola y² - 2x + 6y + 3 =0 with solution please. tnx
a.(-3,3)
b.(3,3)
c.(-3,2)
d.(-3,-3)

guys can you help me to understand this question? how will get it?

Answer 1

Ok, I love these! Let me help you. First of all the equation in standard from for a parabola is either y^2=4xp or x^2 = 4yp. In order to get this into standard form, you need to realize that this is a y^2 parabola, which means that it opens up to either the right or the left (as opposed to up or down). So that means the y terms need to be on one side of the equation and the x terms and constants on the other. When you do this, you get y^2 + 6y = 2x - 3. Now in order to find out the vertex, you need to complete the square on the y^2 term. You take half the x term and square it. Here the x term is 6. Half of that is 3; squaring 3 gets you 9, which you have to add to both sides of the equation. Now you have to get it into a (y +/- ??)^2 to get it into standard form on the left. What number did you square to get 9? 3. So your parenthesis contain the expression (y + 3)^2. That's your y coordinate for the vertex. The x side, the other side of the equation looks like this: 2x - 3 + 9. Add your constants and you get 2x + 6. Factor out a 2 and you get 2(x + 3), which is the x coordinate of the vertex. So, of course you take the opposite sign of what is inside the parenthesis, so your vertex is at (-3, -3). Hope that helps!

Answer 2

can you show me the proper solving to easy to understand?