Final answer:
To find the equation of the quadratic function with a given vertex and point, we use the vertex form of a quadratic equation and solve for the coefficient 'a'. The final equation is y = 6(x + 3)² - 12.
Step-by-step explanation:
To find the equation of a quadratic function with a vertex of (-3, -12) and that passes through the point (-2, -6), we can use the vertex form of a quadratic equation, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Here, h = -3 and k = -12, so the equation starts as y = a(x + 3)² - 12. To find the value of a, we plug in the coordinates of the given point (-2, -6), which gives us -6 = a(-2 + 3)² - 12.
Now solve for a: -6 = a(1)² - 12 => a = 6. Thus, the equation of the quadratic function is y = 6(x + 3)² - 12.