2m^2+2m-12=0 in vertex form

y = 2 (m + 1/2) ^ - 25/2

Step-by-step explanation:

vertex form is:

y = 2m^2 + 2m - 12

y + 12 + () ___ = () 2m^2 + 2m + ___

Because a is not one, you must divide the entire right side by the a value, which is 2. Then place the 2 in the parenthesis.

y + 12 + (2) __ = (2) m^2 + m + __

Take half of b, b being one.

Half of be is 1/2. Now square it to get 1/4. Place that value in the blanks.

y + 12 + (2) 1/4 = (2) m^2 + m + 1/4

Now simplify the left side and factor the right side.

y + 12 + 1/2 = 2 (m + 1/2) ^2

y + 25/2 = 2 (m + 1/2) ^2

Subtract 25/2 from both sides.

y = 2 (m + 1/2) ^ - 25/2