The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. S
how 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)
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)