The question asks us to find the standard form of the quadratic function that has a vertex at (3, 4) and goes through (4, 5).
In order to solve this question, we simply use the general vertex form of a quadratic equation.
The vertex form a quadratic equation is:

We have been given the vertex coordinates as (3, 4).

Thus, the incomplete quadratic equation:

Now, we need to find the value of "a".
In order to find "a", we can use the coordinates that the quadratic graph passes through
i.e. (4, 5)
This is done below:

Now that we have the value of "a", we can write the quadratic equation as:

Therefore, the final answer is:
