If f(x) = (2x + 1)(2x + 3), complete the square and determine the minimum or maximum value of the function

Question

If f(x) = (2x + 1)(2x + 3), complete the square and determine the minimum or maximum value of the function

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Jade 2 weeks 2021-10-14T00:40:05+00:00 1 Answer 0

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    2021-10-14T00:41:10+00:00

    Step-by-step explanation:

    Use FOIL, first outside inside last

    2x × 2x = 4x^2

    2x × 3 = 6x

    1 × 2x = 2x

    1 × 3 = 3

    4 {x}^{2}  + 8x + 3

    The formula to find the minimum or maximum value is

    x =   \frac{ - b}{2a}

    And remember it’s always ax^2 + bx + c

    So now just plug in the numbers

     \frac{ - 8}{2(4)}

    -8/8 = -1

    If a > 0 then the graph is upwards, in this case 4>0 so it is upwards. And -1 is the vertex, which is the minimum value

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