How Do You Convert a Quadratic Equation from Vertex Form to Standard Form?

Vertex form of a quadratic is y = a(x-h)²+k, where (h,k) is the vertex
Standard form of a quadratic is y = ax²+bx+c
Since we have the sum (x+3) being squared, we can use the formula for the square of a sum to save time
The formula for the square of a sum says that (a+b)² = a²+2ab+b²
For the formula, a = x and b = 3, so we get x²+6x+9 when we plug in
Use the Distributive Property to distribute the 2 through the parentheses
y = 2x²+12x-4 is our equation in standard form

1. Right now our equation is in vertex form
2. We want to convert it to standard form
1. Our equation, y = 2(x+3)²-22, is written in vertex form
2. Vertex form is helpful if we want to quickly pick out the vertex of a quadratic equation
3. This makes it a lot easier to graph
4. But usually quadratic equations are easier to solve when they're in standard form
5. In vertex form, the point (h,k) is the vertex
1. The order of operations says that we need to get rid of the parentheses first
2. Since our term in parentheses is being squared, we'll start by simplifying that
1. One way we could simplify (x+3)² is by rewriting it as (x+3)(x+3) and FOILing
2. But luckily, there is a formula we can use when we have a binomial being squared that will save us some trouble!
1. (a+b)² = a²+2ab+b² is the formula for the square of a sum
2. We want to expand out (x+3)²
3. So here we'll let a = x and b = 3
4. Here when we plug in 'x' for 'a' and 3 for 'b' we get x²+2(x)(3)+(3)²
5. If we simplify that, we end up with x²+6x+9
1. To get rid of the last set of parentheses, we need to distribute the 2 into x²+6x+9
1. Multiply 2 by each term inside the parentheses
1. Now all we have to do to finish simplifying is combine like terms!
2. 18 and -22 are both constants, so we can add them to get -4

Write y = 2(x + 3)2 - 22 in standard form.