Set the polynomial equal to to find the properties of the parabola.

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Simplify the right side.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Move the negative one from the denominator of .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raise to the power of .

Multiply by .

Divide by .

Multiply by .

Add and .

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Find the Vertex Form g(x)=-3x^2+30x-74