there are lots of ways to find the vertex. It depends on the way the equation of the parabola is found.
if it is in the form
[tex]y = ax^2 + bx + c[/tex] where a, b, c are constants
1. The vertex is on the line of symmetry of the parabola. this can be found by using
[tex]x = \frac{-b}{2a} [/tex]
then substitute this value into the equation to find the corresponding y value.
e.g. if you have a parabola
[tex]y = -x^2 + 6x + 4[/tex]
a = -6, b = 1 and c = 4
the line of symmetry is
[tex]x = \frac{-6}{2 \times (-1)} = 3[/tex]
the line of symmetry is x = 3 now substitute
[tex]y = -(3)^2 + 6\times 3 + 4 = 13[/tex]
y = 13 is the maximum for the curve.
so the vertex is at (3, 13)
hope it makes sense.
There are other methods that involve completing the square
I just find this easy
