SOLUTION: Form quadratic functions given the following information: Chapter Reference b f(3+ sqrt2 )=f(3−sqrt2 )=0; f(1)=−8

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Question 1109709: Form quadratic functions given the following information:
Chapter Reference
b
f(3+ sqrt2 )=f(3−sqrt2 )=0; f(1)=−8

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The roots are 3+sqrt(2) and 3-sqrt(2); that means the axis of symmetry is x=3; that means the vertex has x coordinate 3. Then the vertex form of the equation is



Then since y is 0 when x is 3+sqrt(2),

(1)

And since y is -8 when x is 1,

(2)

Then from equations (1) and (2)




And then from either equation (1) or (2), k = 8.

So the equation is





Solving this equation using the quadratic formula verifies that the roots are 3 +/- sqrt(2); evaluating the expression for x=1 verifies that the y value is -8.

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