Question

Find the quadratic function y = ax + bx + c whose graph passes through the given points.(1.1), (2.7), (3.19)

Answer 1

Given

points which lie on the function (1,1),(2,7),(3,19)

Find

the quadratic function

Explanation

(1,1) will lie on the function

So,

$\begin{gathered} a(1)^2+b(1)+c=1 \\ a+b+c=1\text{ ----------\lparen1\rparen} \end{gathered}$

(2,7) will lie on the function

$\begin{gathered} a(2)^2+b(2)+c=7 \\ 4a+2b+c=7\text{ ------------\lparen2\rparen} \end{gathered}$

(3,19) will lie on the function

$\begin{gathered} a(3)^2+b(3)+c=19 \\ 9a+3b+c=19----------(3) \end{gathered}$

Solving all these equations

We get a =3, b=-3 and c=1

Final Answer

$f(x)=y=3x^2-3x+1$