Question

How do you find the vertex of a parabola with any given equation?

A detailed explanation is much appreciation:)

Answer 1

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


`y = ax^2 + bx + c` where a, b, c are constants

1. The vertex is on the line of symmetry of the parabola. this can be found by using


`x = (-b)/(2a)`

then substitute this value into the equation to find the corresponding y value.

e.g. if you have a parabola


`y = -x^2 + 6x + 4`

a = -6, b = 1 and c = 4

the line of symmetry is


`x = (-6)/(2 * (-1)) = 3`

the line of symmetry is x = 3 now substitute


`y = -(3)^2 + 6* 3 + 4 = 13`

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