Question

Find a,b, and c if f(0)=5, f(-2)=21 and f(3)=-4 and f(x)=ax^2+bx+c.

Answer 1

if \(f(0)=5\) then \(a\times 0^2+b\times 0+c=5\implies c=5\) so you got one right away

Answer 2

to get the other two, replace \(x\) by \(3\) and set the result equal \(-4\) i.e. write
\[9a+3b+5=-4\] or
\[9a+3b=-9\]

Answer 3

similarly replacing \(x\) by \(-2\) gives
\[4a-2b+5=21\] or
\[4a-2b=16\]

Answer 4

solve the equations
\[9a+3b=-9\\4a-2b=16\] to find \(a\) and \(b\)

Answer 5

\[a=1\] and \[b=-6\]