6.5 Applications
6.5 Solve Problems Using Quadratic Equations
Example 1: The equation h = ­4.9t2 + 60t + 3 represents the path of a rocket that is launched from a 3 meter tall platform. a) How long would the rocket take to fall to the earth?
Objective: Apply our skills of solving quadratic equations and be able to interpret our results!
(0,3)
b) What is the maximum height of the rocket?
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6.5 Applications
Task for today's class: ­ Go to each station and complete the question at the table.
­ Use the hints sparingly! Try it yourself first!
Now let's take up the questions as a class!
Problem #1
One leg of a right triangle is 1 cm longer than the other leg. The length of the hypotenuse is 9cm greater than that of the shorter leg. Find the lengths of the three sides. 2
6.5 Applications
Problem #2
The height of a rocket fired from 1.5 meters above the ground is modeled by the equation h = ‐4.9t2 +49t + 1.5 , where ‘h’ is the height of the rocket in meters, and ‘t’ is the time in seconds. a) After how long does the rocket land on the ground?
b) What is the maximum height of the rocket?
Problem #3:
The length of a rectangle is 16cm greater than its width. The area is 35cm2. Find the dimensions of the rectangle to the nearest meter.
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6.5 Applications
Problem #4
The path of a soccer ball after it is kicked from a height of 0.5 meters above the ground is given by the equation h = ‐0.1d2 + d + 0.5 , where ‘h’ is the height in meters, and ‘d’ is the horizontal distance in meters. a) How far has the soccer ball travelled horizontally when it lands on the ground
b) Find the horizontal distance when the soccer ball is at a height of 2.6 meters above the ground. Complete 6.5 Worksheet
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