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