Question Type 3: Formulating and solving linear equations in coefficients of polynomials Exercises

Determine the equation of the line through $(1,2)$ and $(3,6)$.

Find the equation of the line passing through the points $(4,0)$ and $(3,1)$.

Find the line equation passing through $(-2,5)$ and $(4,-1)$.

Given $q(x)=ax^2+bx+1$ passes through $(1,4)$ and $(2,9)$, find $a$ and $b$.

Find the quadratic $p(x)=ax^2+bx+c$ through points $(1,0)$, $(2,3)$ and $(3,8)$.

Given $s(x)=ax^2+bx-1$ and $s(1)=2$, $s(2)=9$, $s(3)=20$, find $a$, $b$.

Determine the quadratic function $f(x)=ax^2+bx+c$ passing through $(0,1)$, $(1,4)$ and $(2,9)$.

Find the quadratic $f(x)=ax^2+bx+c$ satisfying $f(1)=3$, $f(2)=8$, and $f(-1)=5$.

Find $r(x)=2x^2+bx+c$ given $r(1)=5$, $r(2)=12$, $r(3)=23$.

Find the quadratic $h(x)=ax^2+bx+c$ passing through $(0,-2)$, $(1,1)$ and $(3,7)$.

Determine the quadratic $f(x)=ax^2+bx+c$ with $c=3$ passing through $(1,6)$ and $(2,11)$.