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Wendell also has a water balloon to launch, but he gets turned around and launches his balloon in the wrong direction! The path of his balloon is modeled by the function where is the horizontal distance in yards in front of the goal line and y is the height of the balloon in yards.

  1. Make a complete graph of the function.

    The graph of f(x) = negative the quantity (x + 2) squared + 3.  The vertex of the downward parabola is (negative 2, comma 3). The y intercept is at (0, comma negative 1). The x intercepts are at (negative 3.732, comma 0) and (negative 0.268, comma 0).

  2. What is the domain of the function? What domain makes sense for this context?

    The domain is all real numbers.
    For this context, a reasonable domain would be .

  3. What is the maximum value of the function? What does this tell you about the path of the balloon?

    The maximum value is the greatest -value.

  4. Use your answers from parts (a) through (c) to completely describe the path of the balloon.

    The intercepts are the two places where the balloon is launched and where it lands.