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Math Help - Quadratic Equation

  1. #1
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    Quadratic Equation

    The equation can be in any form (standard, vertex, or intercept)

    A quadratic with zeros at -4 and -1 and y-intercept at -8
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  2. #2
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    Re: Quadratic Equation

    A quadratic can be written in the form y= ax^2+ bx+ c. If "there is a zero at -4", then y= 0 when x= -4: 0= a(-4)^2+ b(-4)+ c. If "there is a zero at -1", then y= 0 when x= -1: 0= a(-1)^2+ b(-1)+ c. If "the y-intercept is at -8" then y= -8 when x= 0: -8= a(0)^2+ b(0)+ c.

    That gives you three equations to solve for a, b, and c.
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  3. #3
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    Re: Quadratic Equation

    Hello, skweres1!

    The equation can be in any form (standard, vertex, or intercept)
    . .
    A quadratic with zeros at \text{-}4 and \text{-}1 and y-intercept at -8.

    With zeros at \text{-}1 and \text{-}4,
    . . the function has the form: . f(x) \:=\:a(x+1)(x+4)

    We are told that f(0) = \text{-}8\!:\;\;a(1)(4) \:=\:\text{-}8 \quad\Rightarrow\quad a \:=\:\text{-}2

    Therefore: . f(x) \:=\:\text{-}2(x+1)(x+4) \:=\:\text{-}2x^2 - 10x - 8
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