Question 118363: Determine the quadratic function which has maximum point (-1,8 ) and x-intercept 3.Express the function in transformational form. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Determine the quadratic function which has maximum point (-1,8 ) and x-intercept 3.Express the function in transformational form.
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If max occurs at (-1,8), -b/2a - -1 ; b = 2a
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You also have the point (3,0)
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EQUATION form
y = ax^2+bx+c
Substituting b = 2a you get:
y = ax^2+2ax+c
Substituting (3,0) you get:
a(3^2)+2*a*3 + c = 0
9a+6a +c = 0
15a+c=0
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Substituting (-1,8) you get:
a((-1)^2)+2*a*-1+c = 8
a-2a+c = 8
-a+c = 8
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Subtracting -a+c=8 from 15a+c=0 you get:
16a = -8
a = -1/2
Then b = -1
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Substituting a=-1/
2 into -a+c=8 you get:
(1/2)+c = 8
c = 15/2
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QUADRATIC EQUATION:
y = (-1/2)x^2-x+(15/2)
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Graph to Check:
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Cheers,
Stan H.
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