What is the equation, in vertex form, of the quadratic function that has a vertex at V(−2, −6) and passes through point P(−4, −7)?

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                         f(x) = a(x - h)² + k

vertex is (-2, -6)  so  h = -2,  k = -6

so:

      f(x) = a(x - (-2))² + (-6)

      f(x) = a(x + 2)² - 6

the parabola goes through the point (-4, -7) so for x=-4,  f(x)=-7

  -7 = a(-4+2)²  - 6

  -7 +6 = a(-2)² - 6 +6

 - 1  = a(4)

     a = -¹/₄

Therefore the equation of the parabola in vertex form:

                                 f(x) = -¹/₄(x + 2)² - 6