• Oct 21st 2009, 01:02 PM
SHiFT
f is a quadratic function such that $f(0) = 0, f(1) = 2,$ and $f(-1) = 2.$ Find an equation for $f(x)$
• Oct 21st 2009, 01:40 PM
pickslides
$f(x) = ax^2+bx+c$

or

$f(x) = a(x-b)^2+c$

Choose one form and use your co-ordinates to substitute and then solve.

Here's a start...

$f(x) = ax^2+bx+c$

$f(0) = 0 \Rightarrow 0 = a\times 0^2+b\times 0 +c \Rightarrow c=0$

So we now have $f(x) = ax^2+bx+0$

$f(1) = 2 \Rightarrow 2 = a\times 1^2+b\times 1 \Rightarrow 2 = a+b$

$f(-1) = 2$
• Oct 21st 2009, 02:05 PM
SHiFT
Okay, well I understand what to do now, but I have some questions. Why for f(1) do you not include c, and I'm assuming for f(-1) you don't include it either. Then after you have solved all of them, do you have to plug them back into the quadratic or can you just leave it as c=0, 2= a+b, etc..
• Oct 21st 2009, 02:19 PM
pickslides
Quote:

Originally Posted by SHiFT
Okay, well I understand what to do now, but I have some questions. Why for f(1) do you not include c,

because we have already found c to be zero

Quote:

Originally Posted by SHiFT
and I'm assuming for f(-1) you don't include it either.

True for the same reason above.

Quote:

Originally Posted by SHiFT
Then after you have solved all of them, do you have to plug them back into the quadratic or can you just leave it as c=0, 2= a+b, etc..

Yep after you have a solution for each a,b and c.

You need to solve for a and b with simultaneous equations first.
• Oct 21st 2009, 02:53 PM
SHiFT
so i need to set a-b and a+b in a equation to solve for them?
• Oct 21st 2009, 02:57 PM
stapel
Quote:

Originally Posted by SHiFT
so i need to set a-b and a+b in a equation to solve for them?

I'm not sure what you mean by this...?

Instead, try using the set-up that the other helper provided to you: Plug the given x-values into the general formula for a quadratic, simplify, and set equal to the given f-values. Solve the resulting system of linear equations by whatever method you prefer of the ones you learned in an earlier algebra course. (Wink)