suppose f(x)=-3x^2 +5x-1 ...vertex form??

Question

i dont understand how to find vertex form ...

need to write f in vertex form, give the vertex

Answer 1

Complete the square
y = -3 x^2 +5x -1 ===> divide by -3 to get coeff of 1
y/-3 = x^2 -5/3 x +1/3 ===> figure out what to add to both sides
(b/2)^2 your b=-5/3 ===> (-5/6)^2 = 25/36

-y/3 + ____ = x^2 - 5/3 x +1/3 + ______
-y/3 + 25/36= x^2 - 5/3 x +25/36 + 1/3
-y/3 + 25/36 = (x - 5/6)^2 + 1/3
-y/3 = (x - 5/6)^2 + 1/3 - 25/36
-y/3 = (x - 5/6)^2 -24/36
y = -3(x-5/6)^2 + 2

vertex form vertex is (5/6, 2)

:)

Answer 2

y =-3x^2+5x-1 = 0
y/-3 = x^2 -5x/3+1/3 = 0
y/-3 =x^2 -5x/3 +25/36 +1/3 =25/36
-y/3 = (x-5/6)^2 -13/36
-y/3 -13/36 = (x-5/6)^2
y - 39/36 = -3(x-5/6)^2
The vertex is (5/6, 39/36) = (5/6,13/12)