Thread: Determining the values of a, b and c for quadratic function given some limits.

Hey, having some problems with this problem. I honestly have no idea how to go about solving it, which is why I came here.

Question:

Determine the real values of a, b, and c for the quadratic function f(x) = ax^2 + bx + c, a cannot equal 0, that satisfy the conditions: f(0) = 0, 'limit as x approaches 1' = 5, and 'limit as x approaches -2' = 8.

I know that these points are in the function, the y intercept is 0 (don't know how that helps), and it looks like there are no discontinuities in this function.

Any help is greatly appreciated!

- Steve

Originally Posted by Kakariki

Hey, having some problems with this problem. I honestly have no idea how to go about solving it, which is why I came here.

Question:

Determine the real values of a, b, and c for the quadratic function f(x) = ax^2 + bx + c, a cannot equal 0, that satisfy the conditions: f(0) = 0, 'limit as x approaches 1' = 5, and 'limit as x approaches -2' = 8.

I know that these points are in the function, the y intercept is 0 (don't know how that helps), and it looks like there are no discontinuities in this function.

Any help is greatly appreciated!

- Steve

Since quadratic functions are continous we know that



Using this fact we get





Solving this system of equations gives

So the desired quadratic is

Originally Posted by TheEmptySet

Since quadratic functions are continous we know that



Using this fact we get





Solving this system of equations gives

So the desired quadratic is

That makes sense, but how do you go about solving the 'system of equations'?

Originally Posted by TheEmptySet

[snip]






[snip]

Originally Posted by Kakariki

That makes sense, but how do you go about solving the 'system of equations'?

The first one is simple.

Substitute the value of c into the second and third equations and simplify them. Now solve those two equations simultaneously