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12 October, 02:18

Consider h (x) = - x2 + 8x + 15. Identify its vertex and y-intercept.

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  1. 12 October, 02:24
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    H (x) = - x² + 8x + 15

    Vertex: h (x) = - x² + 8x + 15

    y = - x² + 8x + 15

    y - 15 = - x² + 8x

    y - 15 = - 1 (x²) - 1 (8x)

    y - 15 = - 1 (x² - 8x)

    y - 15 - 1 (16) = - 1 (x² - 8x + 16)

    y - 15 - 16 = - 1 (x² - 4x - 4x + 16)

    y - 31 = - 1 (x (x) - x (4) - 4 (x) - 4 (4))

    y - 31 = - 1 (x (x - 4) - 4 (x - 4))

    y - 31 = - 1 (x - 4) (x - 4)

    y - 31 = - 1 (x - 4) ²

    y - 31 + 31 = - 1 (x - 4) ² + 31

    y = - 1 (x - 4) ² + 31

    y = - 1 (x + (-4)) ² - (-31)

    h (x) = - 1 (x + (-4)) ² - (-31)

    (h, k) = (4, 31)

    Y-Intercept: h (x) = - x² + 8x + 15

    y = - x² + 8x + 15

    y = - (0) ² + 8 (0) + 15

    y = - (0) + 0 + 15

    y = - 0 + 0 + 15

    y = 0 + 15

    y = 15

    h (x) = 15

    (x, y) = (0, 15)
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