Western Governors University (WGU) MATH1200 C957 Applied Algebra Practice Exam

A characteristic behavior of a quadratic function as x approaches extreme values relates to the shape of its graph, which is a parabola. Quadratic functions take the general form of \( f(x) = ax^2 + bx + c \). Depending on the coefficient \(a\), the parabola opens either upwards or downwards. For a quadratic function that opens upwards (when \( a > 0 \)), as \( x \) approaches positive or negative infinity, the values of \( f(x) \) will increase indefinitely. Specifically, it does not have a maximum value since there is no upper bound; it will keep rising without limit as you move far enough to the right or left along the x-axis. Conversely, for quadratic functions that open downwards (when \( a < 0 \)), the function achieves a maximum value at its vertex, and as \( x \) moves towards positive or negative infinity, the values of \( f(x) \) will decrease indefinitely. In conclusion, the correct answer describes the nature of the parabola's vertex and its extreme behavior correctly. A quadratic function does indeed approach a maximum before decreasing if it opens downwards, illustrating the characteristic behavior that defines the general shape of quadratic functions.