Question

The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for h(x). (2 points)

Answer 1

Given the function h(x)=x^2+14x+41, to solve by completing square we procced as follows;
x^2+14x+41=0
x^2+14x=-41
but;
c=(b/2)^2
and b=14
hence;
c=(14/2)^2=49
substituting the value of c in the expression we get:
x^2+14x+49=-41+49
x^2+14x+49=8
(x+7)^2=8
this can be written in vertex form;
h(x)=a(x-h)^2+k
where:
(h,k) is the vertex;
thus
(x+7)^2=8
h(x)=(x+7)^2-8
hence the vertex will be at the point:
(-7,-8)