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)

please can someone create an actual box


  1. a) h(x) = (x + 7)^2 – 9
    b) the vertex is at (-7, -9) and it is a minimum.
    b) The axis of symmetry is x = -7

    How to rewrite the parabola equation?

    Here we have the parabola equation:
    h(x) = x^2 + 14x + 41
    First, we want to rewrite it in vertex form.
    We can complete squares first, notice that if we add and subtract 8 we will get:
    h(x) = x^2 + 14x + 41 + 8 – 8
    h(x) = x^2 + 14x + 49 – 9
    h(x) = (x^2 + 2*7*x + 7*7) – 9 = (x + 7)^2 – 9
    The parabola in vertex form is:
    h(x) = (x + 7)^2 – 9
    b) The general vertex form is:
    y = (x – h)^2 + k
    Where the vertex is (h, k)
    Then the vertex of our parabola is (-7, -9)
    And because the leading coefficient of our parabola is positive, we can know that the parabola opens upwards, it would mean that the vertex is a minimum.
    c) The axis of symmetry is a vertical line such that x is equal to the x-value of the vertex, then the axis of symmetry is:
    x = -7.
    If you want to learn more about parabolas:


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