To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.
Starting with the vertex form of the equation of a parabola:
y = 2(x - 3)^2 + 5
We can expand the squared term using the square of a binomial formula:
y = 2(x^2 - 6x + 9) + 5
Next, we distribute the coefficient 2:
y = 2x^2 - 12x + 18 + 5
Simplifying the constant terms:
y = 2x^2 - 12x + 23
This is the standard form of the equation of the parabola.