Final answer:
To define a quadratic function that satisfies the given conditions, use the vertex form of a quadratic equation and substitute the given vertex and point. The quadratic function that satisfies the given conditions is y = -1(x + 3)² - 4.
Step-by-step explanation:
To define a quadratic function that satisfies the given conditions, we can use the vertex form of a quadratic equation which is y = a(x - h)² + k, where (h, k) represents the vertex. So, substituting the given vertex (-3, -4) into the equation, we get y = a(x + 3)² - 4. Now, to find the value of 'a', we can substitute the other given point (0, -31) into the equation and solve for 'a'. So, substituting (0, -31), we have -31 = a(0 + 3)² - 4. Solving this equation, we find that a = -1.
Therefore, the quadratic function that satisfies the given conditions is y = -1(x + 3)² - 4.