what's the general formula to find the vertex of an equation. for example: x=2y^2. I can draw the graph and see that the vertex is (0,0), but is there a mathematical way to figure it out?

Question

mathmate · Answer

The general form of a quadratic equation is
y=a(x-h)^2+k
where (h,k) is the vertex.
If the equation is not already in the above (canonical) form, you can convert to that form by completing the squares.

anonymous · Answer

Thank you

mathmate · Answer

You're welcome!

anonymous · Answer

well actually this is a parabola that opens to the right, and cannot be written as 
$$y=a(x-k)^2+h$$ but rather as 
$$x=a(y-k)^2+h$$ but you are right, the vertex is (0,0)

anonymous · Answer

For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k. If you've already learned the Quadratic Formula, you may find it easy to memorize the formula for k, since it is related to both the formula for h and the discriminant in the Quadratic Formula: k = (4ac – b2) / 4a.

anonymous · Answer

at the risk of repeating myself this is 
$$x=2y^2$$ and CANNOT

anonymous · Answer

Find the vertex of y = 3x2 + x – 2 and graph the parabola.
To find the vertex, I look at the coefficients a, b, and c. The formula for the vertex gives me:

h = –b/2a = –(1)/2(3) = –1/6

Then I can find k by evaluating y at h = –1/6:

k = 3( –1/6 )2 + ( –1/6 ) – 2

= 3/36   –  1/6  – 2

=  1/12   –  2/12  –  24/12

=  –25/12

anonymous · Answer

be written as 
$$y=a(x-k)^2+h$$ because the square is on the "y" not on the "x"