The function fx ax2 bx c is a quadratic function where a

The function f(x) = ax^2 + bx + c is a quadratic function, where a, b, and c are constants. If f(-1) = 6, then 6 = a(-1)^2 + b(-1) + c or a - b + c = 6. Find two additional linear equations if f(1) =2 and f(2) = 9. Use the three linear equations found in part (a) to determine a, b, and c. What is the quadratic function that contains the points (-1, 6), (1, 2), and (2, 9)?

Solution

a)Two additional linear equations are given byas follows

f(1)=> If we put 1 in function we get

2=a+b+c

f(2)=>If we put 2in function we get

9=4a+2b+c

b)