Final answer:
The question is about writing a quadratic function in standard form given the vertex and a point on the graph. The vertex form is converted into the standard form by substituting the given vertex and determining the coefficient 'a' using the other provided point.
Step-by-step explanation:
The student is dealing with a quadratic function in standard form, which can be written as f(x) = ax² + bx + c, where a, b, and c are constants, and the vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) represents the vertex. Since the student has the vertex and a point the graph passes through, the standard form can be determined by substituting the vertex into the vertex form, then finding the value of a using the given point.
To write the function in standard form, we need to expand the vertex form, combine like terms, and simplify. Our final equation will provide the values of a, b, and c that define the specific parabola represented by the function.