Final answer:
To find the equation of the quadratic function with vertex (2, 0) and a point (4, 12), we use the vertex form y=a(x-h)^2+k. Plugging in the vertex and solving for 'a' using the known point, the equation of the quadratic function is y = 3(x - 2)^2.
Step-by-step explanation:
The question is asking us to find the equation of a quadratic function with a given vertex and another point on the graph.
We know the vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Since the vertex is given as (2, 0), we can plug these values into the vertex form to give us y = a(x - 2)^2. We now only need to find the value of 'a'.
Given that the point (4, 12) lies on the graph, we can substitute x = 4 and y = 12 into the equation to solve for 'a': 12 = a(4 - 2)^2. Simplifying, we get 12 = 4a, and so, a = 3. Therefore, the equation of the quadratic function is y = 3(x - 2)^2.