Calc Question

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Homework Statement



Find a quadratic function f(x), that satisfies the given conditions: f(1) = 2,
f(-1) = 4, f(3) = 8.

Thanks


Homework Equations



f(x) = k(x-s)(x-t)

The Attempt at a Solution



I tried entering the points as the the x and f(x) while estimating as what the zeroes would be and seeing if k values would be the same but it did not work.

I am pretty sure that the first zero is 2 < x < 4, and the second zero is 4 < x < 8. But I have no idea where to go now. Any help would be greatly appreciated.
 
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Answers and Replies

  • #2
D H
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Homework Equations


f(x) = k(x-s)(x-t)
This is not a good form to use when solving this kind of problem. You get terms like [itex]kst[/itex], which are very hard to deal with. Try using a different form, for example [itex]f(x) = ax^2 +bx + c[/itex].
 
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  • #3
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how do you find a, b and c?
 
  • #4
D H
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Don't use calculus. With that form, what are f(-1), f(1), and f(3)?
 
  • #5
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Is it by trial and error or is there a simpler way to do it?
 
  • #6
cristo
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Is it by trial and error or is there a simpler way to do it?
Just put in each value of x, and you will obtain 3 equations which you can solve for a, b and c.
 
  • #7
D H
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Just put in each value of x, and you will obtain 3 equations which you can solve for a, b and c.
For example, [itex]f(1) = a*1^2 + b*1 + c = a+b+c[/itex]
 
  • #8
HallsofIvy
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This is hardly a "Calc" problem- more like basic algebra

[itex]f(1) = a*1^2 + b*1 + c = a+b+c= 2[/itex]

Do the same with the other two values you are given so you have three equations for a, b, and c. Solve the equations.
 

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