Question

50 POINTS!

The function h(x) = x2 + 6x + 7 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work.

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?

Part C: Determine the axis of symmetry for h(x).

Answer 1

A. (x + 3)² - 2

B. (-3,-2); min

C. x = -3

Explanation:

x² + 6x + 7

x² + 2(x)(3) + 3² - 3² + 7

x² + 2(x)(3) + 3² - 9 + 7

(x + 3)² - 2

Vertex: (-3 , -2)

It's a concave up, so minimum

Line of symmetry is x = h

x = -3