Question

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

Answer 1

`y = 2(x + 1/2 )^2 +23/2`

Explanation:

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

The function `y = 2x^2 + 2x + 12 " is in this form "`

and by comparison , a = 2 , b = 2 and c = 12

The vertex form of the equation is `y = a(x - h )^2 + k`
where (h , k ) are the coordinates of the vertex.

x-coord of vertex (h ) `= (-b)/(2a) = (-2)/4 = -1/2`

and y-coord (k) =`2(-1/2)^2 + 2(-1/2) + 12 = 1/2 - 1 + 12 = 23/2`

here `(h , k ) = (-1/2 , 23/2 ) and a = 2`

`rArr y = 2(x + 1/2 )^2 + 23/2 " is equation in vertex form "`