Final answer:
The given quadratic function f(x) = -x^2 − 3x + 3 is already in the standard form of a quadratic equation, which is ax^2 + bx + c.
Step-by-step explanation:
To express the given quadratic function f(x) = -x^2 − 3x + 3 in standard form, you simply need to rewrite the equation as it already is in the form of at^2 + bt + c where 'a', 'b', and 'c' are constants. The standard form of a quadratic equation is ax^2 + bx + c, and the given function already fits this format with a = -1, b = -3, and c = 3. As a result, standard form for the function already exists.
However, if the student means to convert it to vertex form, which is of the format a(x-h)^2 + k, where '(h,k)' is the vertex of the parabola, the student would need to complete the square to find the vertex form of the quadratic function.