Mathematics 20-2
Angry Birds and Quadratic Functions
Angry Birds Problem
Angry Birds is one of the top-selling apps. It is known worldwide and played by people of all ages. Let's talk about some Mathematics associated with the popular game.
1. Below is a screenshot of a game of Angry Birds. The projectile of the bird forms a parabola. The equation of the parabola can be expressed in the form y = ax²+bx+c. What can you tell about the 'a' value from the graph?
2. A popular reality TV show called 'Survivor' uses challenges to award immunity to one of the tribes. The producers of the show had an idea to simulate the Angry Birds game for one of the challenges. Below is a picture of one such challenge. The path of the bird is modeled by the equation y = -0.039x² +1.68x, where 'y' is the height of the bird, in feet, and 'x' is the horizontal distance, in feet. Answer the questions below.
a) Draw the graph of the function (above) on the grid to the right.
b) What is the positive x-intercept, to the nearest tenth? Will it knock over the smiley face?
(4.28, 6.48)
(12.61, 15.04)
c) What is the maximum height reached by the bird, to the nearest tenth?
d) What is the horizontal distance when the bird reaches maximum height, to the nearest tenth?
1. The 'a' value in the equation y = ax²+bx+c determines the direction of the parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards.
2.
a) The graph of the function y = -0.039x² + 1.68x is a parabola opening downwards.
b) The positive x-intercept occurs when y = 0. To find this, we set y = -0.039x² + 1.68x = 0 and solve for x. The positive x-intercept is approximately 12.6 feet. It will not knock over the smiley face, as the smiley face target is at a height of 6.48 feet.
c) To find the maximum height reached by the bird, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by x = -b/2a. Plugging in the values of a = -0.039 and b = 1.68, we find x ≈ 21.5 feet. Substituting this value back into the equation, we find the maximum height to be approximately 19.4 feet.
d) The horizontal distance when the bird reaches maximum height is given by the x-coordinate of the vertex, which is approximately 21.5 feet.