Question

How do I convert from vertex form to standard form? What is Y = -2(x-2)^2+13 in standard form? PLEASE SHOW WORK!!

a) Y = -2x^2 + 4x + 17
b) Y = -2x^2 - 4x + 13
c) Y = -2x^2 + 4x + 13
d) Y = -2x^2 - 4x + 17

Answer 1

To convert from vertex form to standard form, distribute and expand the equation, and then combine like terms.

Step-by-step explanation:

To convert from vertex form to standard form, we need to expand and simplify the equation.

Starting with the equation Y = -2(x-2)^2+13:

1. Distribute the -2 through the expression (x-2)^2. This gives us Y = -2(x^2-4x+4)+13.
2. Expand the expression -2(x^2-4x+4) by distributing the -2. This gives us Y = -2x^2+8x-8+13.
3. Combine like terms. This gives us Y = -2x^2+8x+5.

So, the equation Y = -2(x-2)^2+13 in standard form is Y = -2x^2+8x+5.