Question

What is the vertex form of `y=x^2-12x+6`?

Answer 1

`y = (x-6)^2 - 30`

Explanation:

The standard form of a quadratic function is `ax^2 + bx + c`

the equation `y = x^2 - 12x + 6 " is in this form "`

with a = 1 , b = -12 and c = 6

The vertex form is : `y = a (x-h)^2 + k`

where (h,k) are the coords of vertex

the x-coord of vertex ( h ) = `(-b)/(2a) = (12)/2 = 6`

and y-coord( k) = `6^2 - 12(6) + 6 = - 30`

now (h , k ) = (6 , -30) and a = 1

`rArr y = (x - 6)^2 - 30 " is vertex form "`