Rewrite the following quadratic fiction in vertex form. Then, determine if it has a maximum or minimum and say what that value is. Y = - x^2 + 6x + 5

First subtract the constant to the other side to simplify it for now

y-5=-x^2+6x

Then pull out a common factor so the coefficient is x^2

y-5=-1 (x^2-6x)

Next you take 1/2 of the b value (-6) and square it to find your c value

[1/2 (-6) ]^2=9

After that plug 9 into your equation as your c value

y-5=-1 (x^2-6x+9)

Adding the C-value (9) causes the equations to become unbalanced so you need to balance them back out by minus 9 to the other side

y-14=-1 (x^2-6x+9)

Now you want to simplify the equation on the right side.

y-14=-1 (x-3) ^2

Finally you want to add the constant back to the right side.

y=-1 (x-3) ^2+14 <-- - vertex form

maximum = (3,14)