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

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)

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Latifah · Answer

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 :  https://brainly.com/question/4061870  #SPJ1

How to rewrite the parabola equation?

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