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Create the equation of a quadratic function in standard form, that has zero’s of {─ 4 and 2} and passes through the point (-1, -18)

 Mar 4, 2021
 #1
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If a quadratic has roots {-4, 2}, then f(-4)=0, f(2)=0, which means

f(x)=ax^2+bx+c

f(-4)=x*(-4)^2+b*(-4)+c=0

f(2) = x*(2)^2+b*(2)+c=0

-18=x*(-1)^2-b+c


solve the system of three, unkowns, then plug the values of a, b, c into ax^2+bx+c

 Mar 4, 2021
 #2
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Zeroes at  -4 and 2   looks like this

    y = a ( x+4)(x-2)   

     y  = a ( x^2 + 2x-8)         sub in the point given to calculate a

    - 18 = a (1 -2 -8)

         a = 2

 

y =   2 x^2 + 4x -16

 Mar 4, 2021

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