Form a quadratic function f(x) for which f(1)=0, f(−1)=−4, and f(2)=5.

Question

Form a quadratic function f(x) for which f(1)=0, f(−1)=−4, and f(2)=5.

Pls help, really confused

Form a quadratic function f(x) for which f(1)=0, f(−1)=−4, and f(2)=5.

Answer 1

Note f(1) = 0 makes 1 a root of f(x) = 0.  That means there is a factor of (x - 1) in f(x).  Since f(x) is also a quadratic function, it can be expressed as

 

f(x) = A(x - 1)(x + k)

 

where A and k are unknown, and A ≠ 0. Substitute the numbers from (-1,-4) and (2,5), and then solve 2 equations in 2 unknowns A and k. Expand, simplify, and get a final form for f(x) as

 

f(x) = ax² + bx + c

 

Note that a = A.

Answer 2

You should not be confused by this.  The function is f(x) = ax² + bx + c

 

and you have three given points (1,0)  (-1,-4)  and  (2,5).

 

If you substitute these you wind up with three equations with unknowns a, b and c.

 

You should be able to solve that system of 3 linear equations by any of several methods that you have learned in Algebra II.