PARABOLAS IN VERTEX FORM

To find vertex of a parabola convert it into vertex form.

y = a (x - h )² + k

Point (h, k) is the vertex of the parabola.

 Example 1:

Find the vertex of the parabola

y = x ² + 4 x + 6

y = x ² + 4 x  + 4 - 4 + 6

y = (x ² + 4 x  + 4) - 4 + 6

y = (x + 2 )² + 2

y = (x - - 2 )² + 2

The vertex of the above parabola

is at (-2,2)

Example 2:

Find the vertex of the parabola

y = 2x ² + 8 x - 12

y = 2(x ² + 4 x      )-12

y = 2(x ² + 4 x  +  4    ) -8 -12

y = 2(x + 2 )² - 20

The vertex of the above parabola

is at (-2,-20)