Find the Function Rule table[[x,y],[0,5],[3,4],[5,3.2]]

Rewrite the equation as ${\displaystyle b=5}$.

Replace all occurrences of ${\displaystyle b}$ with ${\displaystyle 5}$ in each equation.

Solve for ${\displaystyle a}$ in ${\displaystyle 3.2=5a+5}$.

Replace all occurrences of ${\displaystyle a}$ with ${\displaystyle -0.36}$ in each equation.

Since ${\displaystyle 4=3.92}$ is not true, there is no solution.

Solve for ${\displaystyle c}$ in ${\displaystyle 5=a\cdot 0^2+c}$.

Replace all occurrences of ${\displaystyle c}$ with ${\displaystyle 5}$ in each equation.

Solve for ${\displaystyle a}$ in ${\displaystyle 3.2=25a+5b+5}$.

Replace all occurrences of ${\displaystyle a}$ with ${\displaystyle -\frac{b}{5}-0.072}$ in each equation.

Solve for ${\displaystyle b}$ in ${\displaystyle 4=1.2b+4.352}$.

Replace all occurrences of ${\displaystyle b}$ with in each equation.

List all of the solutions.

Calculate the value of ${\displaystyle y}$ such that ${\displaystyle y=a{x}^2+b}$ when , , ${\displaystyle c=5}$, and ${\displaystyle x=0}$.

If the table has a quadratic function rule, ${\displaystyle y=y}$ for the corresponding ${\displaystyle x}$ value, ${\displaystyle x=0}$. This check passes since ${\displaystyle y=5}$ and ${\displaystyle y=5}$.

Calculate the value of ${\displaystyle y}$ such that ${\displaystyle y=a{x}^2+b}$ when , , ${\displaystyle c=5}$, and ${\displaystyle x=3}$.

If the table has a quadratic function rule, ${\displaystyle y=y}$ for the corresponding ${\displaystyle x}$ value, ${\displaystyle x=3}$. This check does not pass, since ${\displaystyle y=4}$ and ${\displaystyle y=4}$. The function rule can\'t be quadratic.

Since ${\displaystyle y\ne y}$ for the corresponding ${\displaystyle x}$ values, the function is not quadratic.