Final answer:
To create a function that has a vertex of (-3, -6) and passes through the point (-4, -3), you can use the vertex form of a quadratic function: y = a(x - h)^2 + k. By substituting the given values into the equation, you can find the value of 'a' and write the equation of the function.
Step-by-step explanation:
To create a function with a vertex of (-3, -6) and passes through the point (-4, -3), we can use the vertex form of a quadratic function, which is y = a(x - h)^2 + k. Substituting the given vertex into the equation, we have y = a(x + 3)^2 - 6. To find the value of 'a', we substitute the coordinates of the other point into the equation. Therefore, -3 = a(-4 + 3)^2 - 6. Solving this equation gives us a value of 'a = 1/4'.
Now, we can write the equation of the function as y = (1/4)(x + 3)^2 - 6. This function has a vertex of (-3, -6) and passes through the point (-4, -3).