# Algebra Examples

To find if the table follows a function rule, check to see if the values follow the linear form .

Build a set of equations from the table such that .

Calculate the values of and .

Solve for in the first equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the second equation.

Simplify.

Simplify the right side.

Multiply by .

Add and .

Simplify the right side.

Multiply by .

Add and .

Simplify the right side.

Multiply by .

Add and .

Solve the third equation.

No solution

List the solutions to the system of equations.

No solution

No solution

No solution

No solution

Calculate the value of using each value in the relation and compare this value to the given value in the relation.

Calculate the value of when , , and .

Simplify each term.

Multiply by .

Multiply by .

Add and .

If the table has a linear function rule, for the corresponding value, . This check passes since and .

Calculate the value of when , , and .

Simplify each term.

Multiply by .

Multiply by .

Add and .

If the table has a linear function rule, for the corresponding value, . This check passes since and .

Calculate the value of when , , and .

Simplify each term.

Multiply by .

Multiply by .

Add and .

If the table has a linear function rule, for the corresponding value, . This check does not pass, since and . The function rule can't be linear.

Since for the corresponding values, the function is not linear.

The function is not linear

The function is not linear

The function is not linear

To find if the table follows a function rule, check whether the function rule could follow the form .

Build a set of equations from the table such that .

Calculate the values of , , and .

Solve for in the first equation.

Solve for in the second equation.

Solve for in the third equation.

Simplify.

Divide by .

Simplify the right side.

Simplify each term.

Multiply by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Multiply by .

Add and .

Simplify the right side.

Multiply by .

Add and .

Solve the fourth equation.

Always true

Remove any equations from the system that are always true.

Calculate the value of using each value in the table and compare this value to the given value in the table.

Calculate the value of such that when , , , and .

Simplify each term.

Multiply by .

Remove parentheses around .

One to any power is one.

Multiply by .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

If the table has a quadratic function rule, for the corresponding value, . This check passes since and .

Calculate the value of such that when , , , and .

Simplify each term.

Multiply by .

Remove parentheses around .

Raise to the power of .

Multiply by .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

If the table has a quadratic function rule, for the corresponding value, . This check passes since and .

Calculate the value of such that when , , , and .

Simplify each term.

Multiply by .

Remove parentheses around .

Raise to the power of .

Multiply by .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

If the table has a quadratic function rule, for the corresponding value, . This check passes since and .

Calculate the value of such that when , , , and .

Simplify each term.

Multiply by .

Remove parentheses around .

Raise to the power of .

Multiply by .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

Since for the corresponding values, the function is quadratic.

The function is quadratic

The function is quadratic

The function is quadratic

Since all , the function is quadratic and follows the form .