Final answer:
The function f(x) = -2x² + 5x - 7 is already simplified as there are no like terms to combine or factor. It represents a parabola that opens downwards.
Step-by-step explanation:
The student has asked to simplify the quadratic function f(x) = -2x² + 5x - 7. To simplify a quadratic function, we usually look for terms that can be combined or factored; however, in this case, the function is already in its simplest form since there are no like terms to combine, and it cannot be factored easily. This quadratic function represents a parabola that opens downwards, as the coefficient of the x² term is negative; namely, -2.
When simplifying algebraic expressions, it's essential to eliminate terms wherever possible and check if the answer is reasonable. If faced with an equation rather than a function, one might need to rearrange the equation to solve for x using methods such as factoring or applying the quadratic formula.