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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