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F asked in Science & MathematicsMathematics · 1 month ago

Find an equation for a polynomial of degree 2 with the following properties: Zeros: x=5 and x=-8F(0)=480?

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  • 1 month ago
    Favorite Answer

    Two zeros:

    x = 5

    x = -8

    Rewrite those as equations equal zero:

    x - 5 = 0

    x + 8 = 0

    Multiply the expressions together:

    y = (x - 5)(x + 8)

    But we can also multiply that by a constant 'a' and it doesn't change the zeros:

    f(x) = a(x - 5)(x + 8)

    Next we are told that f(0) = 480:

    480 = a(0 - 5)(0 + 8)

    480 = a(-5)(8)

    480 = -40a

    a = 480/-40

    a = -12

    So there's our final function:

    f(x) = -12(x - 5)(x + 8)

    If they want you to, you should expand that out:

    f(x) = -12(x² + 8x - 5x - 40)

    f(x) = -12(x² + 3x - 40)

    Answer:

    f(x) = -12x² - 36x + 480

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  • 1 month ago

    y = (480/(5*-8))(x - 5)(x - 8) is an equation, as is y = -12x² + 156x - 480

    Source(s): The parabola with non-zero x-intercepts: x₀, x₁, and non-zero y-intercept: y₀ is y = (y₀/(x₀ x₁))(x - x₀)(x - x₁).
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  • ted s
    Lv 7
    1 month ago

    y = A ( x - 5 )(x + 8) where A = 480 / (-40)

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