Question

Given the following three points, find by hand the quadratic function they represent.

Answer 1

let the function be $y=ax^2+bx+c$

put $x=0, \, y=6$ , to get $c=6$

put $x=2, \, y=16$ , $16=4a+2b+6\implies 2a+b=5$

put $x=3, \, y=33$ , $33=9a+3b+6\implies 3a+b=9$

subtract the two equation, to get $a=4$

now substitute $a$ in first equation, to get $b=5-2\cdot4=-3$

so, $f(x)=4x^2-3x+6$