Answer:
see explanation
Explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 3x² + 12x - 7 ← factor out 3 from the first 2 terms
= 3(x² + 4x) - 7
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 4x
f(x) = 3(x² + 2(2)x + 4 - 4) - 7
= 3(x + 2)² - 3(4) - 7
= 3(x + 2)² - 12 - 7
= 3(x + 2)² - 19 ← in vertex form
with vertex = (- 2, - 19 )