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5 June, 17:21

What is the vertex of the function f (x) = 4x2 + 3x + 3?

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  1. 5 June, 17:48
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    the vertex is at (h, k) = > (-3/8, 39/16)

    Step-by-step explanation:

    One way of determining the vertex location is to "complete the square."

    f (x) = 4x2 + 3x + 3 can be rewritten as

    f (x) = 4 (x^2 + (3/4) x) + 3

    We complete the square of (x^2 + (3/4) x) as follows:

    (x^2 + (3/4) x + 9/64 - 9/64) or

    (x + 3/8) ^2 - 9/64

    Now re-write f (x) = 4 (x^2 + (3/4) x) + 3 (from above) as

    f (x) = 4 ((x + 3/8) ^2 - 9/64) + 3, or

    f (x) = 4 (x + 3/8) ^2 - 9/16 + 48/16, or

    f (x) = 4 (x + 3/8) ^2 + 39/16

    Comparing this to the standard vertex equation

    f (x) = a (x - h) ^2 + k, we see that h must be - 3/8 and k must be 39/16.

    Thus, the vertex is at (h, k) = > (-3/8, 39/16).
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