College Math
posted by Ginger on .
Find the vertex and axis of symmetry of the graph of a function.
f(x)=x^2+6x+16

f(x) = x^2+6x+16
= x^2 +6x +9 +3
= (x+3)^2 +3
The vertex (lowest point) is x= 3, y = 3. That is because (x+3)^2 can never ne negative.
It is symmetrical about the x=3 vertical line. 
f(x) = x^2 + 6x + 16.
h = Xv = b / 2a = 6 / 2 = 3,
Substitute 3 for x in the given Eq:
k = Yv = (3)^2 + 6*3 16,
k = 9  18 + 16 = 25  18 = 7,
V(h , k) = V(3 , 7).
Axis: h = Xv = 3. = A vertical line
where x isconstant at 3 for all values of y.