Label the vertex of this functiony=-3(x-1)(x+4):

Question

Label the vertex of this functiony=-3(x-1)(x+4):

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Calantha 5 months 2021-08-15T00:24:04+00:00 1 Answers 3 views 0

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    2021-08-15T00:25:22+00:00

    Answer:

    vertex = ( – \frac{3}{2},  \frac{75}{4} )

    Step-by-step explanation:

    Given a parabola in standard form

    y = ax² + bx + c ( a ≠ 0 )

    Then the x- coordinate of the vertex is

    x_{vertex} = – \frac{b}{2a}

    Given

    y = – 3(x – 1)(x + 4) ← expand the factors using FOIL

      = – 3(x² + 3x – 4) ← distribute parenthesis by – 3

      = – 3x² – 9x + 12 ← in standard form

    with a = – 3 and b = – 9 , thus

    x_{vertex} = – \frac{-9}{-6} = – \frac{3}{2}

    Substitute this value into the equation for corresponding value of y

    y = – 3( – \frac{3}{2} – 1)( – \frac{3}{2} + 4)

      = – 3 × – \frac{5}{2} × \frac{5}{2}

      = – 3 × – \frac{25}{4}

      =  \frac{75}{4}

    Thus

    vertex = ( – \frac{3}{2}, \frac{75}{4} )

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