Question

Problem 3 – A pancake in the air? An application of a parabola at breakfast time! Think about how a pancake rises slightly before it falls back to land on the griddle. Have you ever flipped a pancake? Have you ever seen a chef toss a pizza crust? Enter the equation Y1 = –4.9x2 + 3.5x + 0.45 in your calculator. Change you window settings to match those at the right.  What is the path the pancake actually travels?  How does the path of the pancake compare to the graph shown? Graph the given equation. Press  to explore the function. As you trace, ordered pairs will appear that represent a time in seconds, and the height of the pancake above the griddle at that time.  Record several ordered pairs here: (you should round to the nearest tenth) Time (sec) Height (cm)  Use the Maximum feature under   to find the maximum height of the pancake, and when it occurs. Enter a left bound, press , enter a right, bound, press , give a guess and press  again. Time (sec): _______ Maximum height (cm): _______  At what time does the pancake land on the hot griddle? Where is this on the graph? Use the Zero feature under   to approximate the point when the pancake lands. Time (sec): _______ Height (cm): _______ (sizzle...Yum!)  The pancake graph is a parabola because “what goes up must come down.” True or false?

Answer 1

1. The path of the pancake is modeled by the equation Y=−4.9x^2+3.5x+0.45.

2. The path of the pancake, as traced by the graph, aligns with the parabolic shape of the equation.

3. Example ordered pairs: (1.0, 2.1), (2.0, 4.2), (3.0, 3.6)...

4. Time (sec): 1.8, Maximum height (cm): 4.0.

5. Time (sec): 0.7, Height (cm): 0.0 (on the griddle).

6. The given statement "the pancake graph forms a parabola, representing its upward trajectory and eventual descent" is true.

1. The equation Y=−4.9x^2+3.5x+0.45 describes the path of the pancake. It is a quadratic equation in the form ax^2 +bx+c, where Y represents the height above the griddle, and x is the time in seconds.

2. When graphed, the path of the pancake, as described by the equation, matches the parabolic shape typically associated with objects under gravity. The trajectory rises before descending, resembling the motion of a tossed pancake.

3. Ordered pairs represent points on the graph, indicating the time (in seconds) and the corresponding height (in centimeters) of the pancake above the griddle. These pairs provide specific data points for analysis and interpretation.

4. Using the Maximum feature, you can find the vertex of the parabola, which represents the maximum height of the pancake. In this example, the maximum height occurs at 1.8 seconds, reaching 4.0 centimeters above the griddle.

5. The Zero feature helps identify when the pancake lands on the griddle, corresponding to the time when the height is 0.0 centimeters. In this case, the pancake lands at 0.7 seconds.

6. The statement "The pancake graph is a parabola because 'what goes up must come down'" is true. A parabola is a suitable mathematical model for the pancake's trajectory, adhering to the principle that objects thrown into the air will follow a parabolic path due to gravity.