Question

Determine the vertex by completing the square. Show process.

y = x2 -6x + 22

Answer 1

(3,13)

Explanation:

`y=x^2-6x+22\\y=x^2-6x+22+3^2-3^2\\y=(x-3)^2+22-9\\y=(x-3)^2+13`

Note that by vertex form we have:

`y=a(x-h)^2+k`

Where the vertex has the coordinates (h,k) so we change the sign of h and keep the same k value and so:

h=3 and k=13

Therefore the vertex of this parabola is: (3,13)