Write the quadratic function in the form:
f(x) = a(x-h)² + k
Given Function:
f(x) = 3x² + 18x + 28
Using the completing square method:
f(x) = 3(x² + 6x + 28/3)
f(x) = 3(x² + 6x + (3)² - (3)² + 28/3)
f(x) = 3[(x+3)² - (3)² + 28/3]
f(x) = 3[(x+3)² - 9 + 28/3]
f(x) = 3[(x+3)² - 27/3 + 28/3]
f(x) = 3[(x+3)² - 1/3]
f(x) = 3(x+3)² - 1
Therefore,
The vertex is (h,k) = (-3,-1)