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30 March, 08:47

Express 2x^2+8x+3 in the form 2 (x+p) ^2+q

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Answers (1)
  1. 30 March, 12:17
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    2 (x + 2) ² - 5

    Step-by-step explanation:

    Given

    2x² + 8x + 3

    To obtain the required form use the method of completing the square.

    The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x

    = 2 (x² + 4x) + 3

    add/subtract (half the coefficient of the x - term) ² to x² + 4x

    = 2 (x² + 2 (2) x + 4 - 4) + 3

    = 2 (x + 2) ² - 8 + 3

    = 2 (x + 2) ² - 5

    with p = 2 and q = - 5
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