Answer:
y = - 3(x - 2)² + 2
Explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) is the coordinates of the vertex and a is a multiplier
given
y = - 3x² + 12x - 10
before completing the square we require the coefficient of the x² term to be 1.
factor out - 3 from the first 2 terms
y = - 3(x² - 4x) - 10
to complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
y = - 3(x² + 2(- 2)x + 4 - 4 ) - 10
y = - 3(x - 2)² - 3(- 4) - 10
y = - 3(x - 2)² + 12 - 10
y = - 3(x - 2)² + 2 ← in vertex form