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16 March, 20:48

The function f (t) = t2 + 12t - 18 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 f (t).

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  1. 16 March, 23:34
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    For

    f (x) = a (x-h) ²+k

    vetex is (h, k)

    axis of symmetry is x=h

    when a is positive, the graph opens up and the vertex is a minimum

    when a is negative, the graph opens down and the vertex is a maximum

    f (t) = (t²+12t) - 18

    take 1/2 of 12 and square it and add negative and positive of it inside (36)

    f (t) = (t²+12t+36-36) - 18

    factoer perfect square

    f (t) = ((t+6) ²-36) - 18

    expand

    f (t) = (t+6) ²-36-18

    f (t) = (t+6) ²-54

    vertex form

    f (t) = 1 (t - (-6)) ² + (-54)

    vertex is (-6,-54)

    1 is positive, it is a minimum

    axis of symmetry is x=-6

    A. f (t) = (t+6) ²-54

    B. (-6,-54), minimum

    C. x=-6
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