Consider the quadratic function

Question

f(x) = x^2 + 12x + 40. Find the vertex.

Answer 1

complete the square,

f(x) = x^2 + 12x + 40
= x^2 + 12x + 36 - 36 + 40
= (x+6)^2 + 4

so the vertex is (-6,4)

or

the x co-ordinate of the vertex for
f(x) = ax^2 + bx + c is -b/(2a)

so x = -12/2 = -6
sub x=-6 back into the function to find f(-6) = 36 - 72 + 40 = 4

or, if you know Calculus,
f'(x) = 2x + 12 = 0 at the vertex
2x + 12 = 0
x = -6 etc

Answer 2

Thank you! I got many more of these to do, so just wanted to make sure my first one was correct! Thanks!