Question

Can u help me with this question nd 1 , 11

Answer 1

In order to find the values of a, b and c, we need to use the three ordered pairs given in the equation and solve the system with 3 variables and 3 equations:

`\begin{gathered} y=ax^2+bx+c \\ (-2,-1)\colon \\ -1=4a-2b+c \\ (1,11)\colon \\ 11=a+b+c \\ (2,27)\colon \\ 27=4a+2b+c \end{gathered}`

Adding the first and third equations:

`\begin{gathered} 26=8a+2c \\ 13=4a+c \\ c=13-4a \end{gathered}`

Using this value of c in the first and second equations:

`\begin{gathered} -1=4a-2b+13-4a \\ -1=-2b+13 \\ 2b=13+1 \\ 2b=14 \\ b=7 \\ \\ 11=a+b+13-4a \\ 11=a+7+13-4a \\ 11=-3a+20 \\ 3a=20+11 \\ 3a=31 \\ a=(31)/(3) \end{gathered}`

Calculating the value of c:

`\begin{gathered} c=13-4a \\ c=13-4\cdot(31)/(3) \\ c=13-(124)/(3) \\ c=(39-124)/(3) \\ c=-(85)/(3) \end{gathered}`

So we have a = 31/3, b = 7 and c = -85/3.