How do I find a polynomial function whose graph passes through each set of points? (-2,-16), (3,11), and (0,2)
Assume it is a linear function, f(x)=ax+b. So f(0)=2, so b=2, so f(x)=ax+2. Then f(-2)=-2a+2=-16, so a=9. f(3)=11 so 3.9+2=29 but not 11.
Assume it is a quadratic function, f(x)=ax^2+bx+c. We have f(0)=c=2. SO f(x)=ax^2+bx+2. f(-2)=4a-2b+2=-16, so 4a-2b=-18, 2a-b=-9. f(3)=11, so 9a+3b+2=11, 3a+b=3. Multiply the second by 2 and add we get 10a=-12, a=-(6/5), b= 3+18/5=33/5.