What is f(x) = 4x^2 - 24x + 31 in vertext form and what is the vertex?

Question

What is f(x) = 4x^2 - 24x + 31 in vertext form and what is the vertex?

Answer 1

vertex form is something like this:

http://www.purplemath.com/modules/sqrver...

Answer 2

f(x) = 4x^2 - 24x + 31

f(x) = 4(x^2 - 6x +31/4)

add and subtract (1/2 *coeff of x)^2 inside the bracket

f(x) = 4[ (x^2 -6x +9) + (31/4 -9) ]

f(x) = 4[ (x-3)^2 - 5/4]

f(x) = 4(x-3)^2 - 5

comparing with the standard equation in vertex form

y = a (x-h) +k   where (h,k) is the vertex

here a=4, h = 3, k = -5

so, the vertex is (3, -5)