Answer:
y = 3(x -2)² -5
Explanation:
It looks like you want to write the standard-form quadratic ...
y = 3x² -12x +7
in vertex form.
The process is similar to that of "completing the square."
Steps
Factor out the leading coefficient
Do this for the variable terms only.
y = 3(x² -4x) +7
Identify the x-term coefficient
The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.
x coefficient: -4
binomial constant: -4/2 = -2
square of this: (-2)² = 4
Add this inside parentheses
To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.
y = 3(x² -4x +4) +7 -3(4)
Simplify to vertex form
Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.
y = 3(x -2)² -5