Answer:
19 - 3(x - 2)²
Explanation:
7 + 12x - 3x² ( rearrange terms in x )
7 - 3x² + 12x ( factor out - 3 from each of the x- terms )
= 7 - 3(x² - 4x)
using the method of completing the square on x² - 4x
add/subtract ( half the coefficient of the x- term )² to x² - 4x
= 7 - 3(x² + 2(- 2)x + 4 - 4)
= 7 - 3(x - 2)² - 3(- 4)
= 7 - 3(x - 2)² + 12
= 19 - 3(x - 2)² ← in the form a + b(x + c)²
with a = 19 , b = - 3 , c = - 2