9.2. The graphs of the functions $y=a x^{2}+b x+1$ and $y=x^{2}+c x+d$ intersect at the point with coordinates ( $2 ; 4$ ). What is the value of the expression $4 a+d$, if $b+c=1$ ?
Answer: 1.

Solution: Since the graphs pass through the point with coordinates (2; 4), then $4=4a+2b+1$ and $4=4+2c+d$. Therefore, $4a+2b=3$, and $2c+d=0$, or $4a=3-2b, d=-2c$. Summing up the obtained expressions: $4a+d=3-2b-2c=3-2(b+c)=3-2=1$. Note: The condition is satisfied by the functions $y=ax^2+bx+1$ and $y=x^2+cx+d$ when $a=1, b=-1/2, c=3/2, d=-3$.

Criteria: Only the answer - 0 points. If the solution is found by selecting suitable values of $a, b, c$ and $d-3$ points. Correctly found values of the expressions $4a+2b=3$ and $2c+d=0$, but no further progress in the solution (or incorrect further solution) - 4 points. 7 points for a complete and correct solution.