Quadratic Real Life Problems Assignment
1. The Football Problem:
When a football is punted (kicked), it goes up into the air, reaches a maximum height, then comes back down. If “t” represents the time in seconds since the ball was kicked and “d” represents the height of the ball in metres, the following equation models the situation.
d = -16t2 + 40t + 4
a)Graph the function on your calculator. Draw below. Identify on the graph the vertex, the y-intercept, and the x-intercepts. Label the axes.
NOTE: d is “y” and t is “x”. You can use your calculator: y = -16x2+ 40x + 4
Window:
xmin = -2xmax = 10xscl = 1ymin = -30ymax = 20yscl = 5
b)Find the coordinates of the vertex on your calculator: ______
c)What does the vertex represent? Answer in sentences.
d)What is the y-intercept? Solve by hand.
e)What does the y-intercept mean or represent? Use sentences!
f)Find the x-intercepts. Solve by hand.
g)When will the ball hit the ground?
2. The Artillery Problem
Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. In order to avoid hitting the mountain on the other side of the river, they have set their cannon on a path described by the equation below:
y = -80x2 + 120x + 610
a) Graph the function on your calculator. Draw below. Identify on the graph the vertex, the y-intercept, and the x-intercepts. Label the axes.
Window:
xmin = -10xmax = 10xscl = 1ymin = -10ymax = 700yscl = 50
b)Find the coordinates of the vertex on your calculator: ______
c)What does the vertex represent? Answer in sentences.
d)What is the y-intercept? Solve by hand.
e)What does the y-intercept mean or represent? Use sentences!
f)Find the x-intercepts. Solve by hand.
g)What do the x-intercepts mean? Answer in sentences.
h)A plane is flying at 660m above the river. Is it in danger of being hit by projectiles fired along this path? (HINT: does y ever equal 660? Use your table on the calculator).
- Cost of Operating a Car Problem
The number of cents per kilometre it costs (C) to drive a car depends on how fast (S) you drive it. At low speeds the cost is high because the engine operates inefficiently. At high speeds, the cost is high because the engine must overcome high wind resistance. At moderate speeds the cost reaches a minimum. This is modelled by the equation:
C = 0.01 S2 – S + 37
C represents the Cost in cents of driving the car per kilometre.
S represents the Speed you are driving the car.
a) Graph the function on your calculator. Draw below. Identify on the graph the vertex, the y-intercept, and the x-intercepts. Label the axes.
NOTE: Rewrite as y = 0.01x2 – x + 37
Window:
xmin = -10xmax = 100xscl = 10ymin = -20ymax = 50yscl = 10
b)Find the coordinates of the vertex on your calculator: ______
c)What does the vertex represent? Answer in sentences.
d)Find the x-intercepts using your calculator.
e) The least number of cents per kilometre (Cost or y) occurs when you get the most kilometres per litre of gas. If your tank were nearly empty, at what speed should you drive to have the best chance of making it to a gas station before you run out?