Find $a,b,c$ if $f(4)=1, f(-2)=14, f(5)=-2$ and $f(x)=ax^2 + bx + c$

Question

Would anyone please explain to me the steps needed in order to find $a,b,c$? I understand I must use elimination, but the answers I keep on getting are very unrealistic. Thanks in advance.

Answer 1

HINT

Just consider the conditions

• $f(4)=1 \implies 16a+4b+c=1$
• $f(-2)=14 \implies \ldots$
• $f(5)=-2 \implies \ldots$

and solve the linear system you obtain to find $a$,$b$ and $c$.

Answer 2

Hint: Solve the system $$f(4)=16a+4b+c=1$$ $$f(-2)=4a-2b+c=14$$ $$f(5)=25a+5b+c=-2$$ for $$a,b,c$$