need help solving this

Question

A quadratic function f is given.

f(x) = −3x2 + 6x − 1

(a)

Express f in vertex form.

Answer 1

-3(x-1)^2 + 2 is vertex form of

-3x^2 +6x -1

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

complete the square

take half the x coefficient and square it

then add and subtract it's value = -3(+1) = -3 and also add +3

= -3(x^2 - 2x +1) -1 +3

= -3(x-1)^2 +2

vertex = (1,2)= maximum point

vertex form is a(x-h)^2 + k, where (h,k) = vertex = (1,2) in this problem. it's a maximum as a= -3 <0

Answer 2

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