Finding a Quadratic Function to Satisfy Conditions

[mathmann]

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.

 

[D H]

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 $kst$, which are very hard to deal with. Try using a different form, for example $f(x) = ax^2 +bx + c$.

 

[mathmann]

how do you find a, b and c?

 

[D H]

Don't use calculus. With that form, what are f(-1), f(1), and f(3)?

 

[mathmann]

Is it by trial and error or is there a simpler way to do it?

 

[cristo]

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.

 

[D H]

Just put in each value of x, and you will obtain 3 equations which you can solve for a, b and c.

For example, $f(1) = a*1^2 + b*1 + c = a+b+c$

 

[HallsofIvy]

This is hardly a "Calc" problem- more like basic algebra

$f(1) = a*1^2 + b*1 + c = a+b+c= 2$

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