Question 919274
Rethink the points which are given.  A vertex maximum should occur between x=0 and x=4, and thinking visually or plotting on paper, you should understand and expect because of this maximum vertex, coefficient on x^2 will be a negative value.


Not seeing any more convenient method, form a system of three equations using the points.


y=ax^2+bx+c


{{{system(a*0^2+b*0+c=1.8,a*2^2+b*2+c=4,a*4^2+b*4+c=3)}}}


{{{system(0*a+0b+c=1.8,4a+2b+c=4,16a+4b+c=3)}}}


Just substitute for c and obtain a system of two equations in a and b.
{{{system(4a+2b+1.8=4,16a+4b+1.8=3)}}}
-
{{{system(4a+2b=2.2,16a+4b=1.2)}}}


Preparing for start of Elimination Method,
{{{system(8a+4b=4.4,16a+4b=1.2)}}}
SUBTRACT the first equation from the second equation,
{{{8a+0b-3.2}}}
{{{8a=-3.2}}}
{{{a=-3.2/8}}}, and multiply by 5, just to simplify into a rational number.
{{{a=-16/40}}}
{{{a=-4/10}}}
{{{highlight(a=-2/5)}}} and already was found {{{highlight(c=1.8)}}}.


Pick either equation from the two-equation, two variable system to solve for b.
{{{4a+2b=2.2}}}
{{{2b=2.2-4a}}}
{{{b=1.1-2a}}}
{{{b=1.1-2(-2/5)}}}
{{{b=1.1+4/5}}}
{{{b=1.1+0.8}}}
{{{highlight(b=1.9)}}}