Warm­up On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket’s height, h, in feet above the surface of the lake is given by the equation h=‐16t2 + 64t + 80, where t is time in seconds.
(a) What is the maximum height of the rocket? (b) How long does it travel upward before its engine burns out? (c) After how many seconds will the rocket hit the lake?
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Quadratic Word Problems
1. The sides of a square are altered so that one is increased by 4 and the other is decreased by 2. The area of the new shape is 27 ft2. What was the area of the original square?
2. A right triangle has a longer leg that is 1 unit longer than its shortest leg. Its hypotenuse is 2 units longer than the shortest leg. Using the Pythagorean Theorem, find the dimensions of the original triangle. 3. When the square of a certain number is decreased by 9 times the number the result is 22. Find the number.
Consecutive Integer Problem
Integer:
Consecutive Integers:
Consecutive even/odd integers:
The product of two consecutive odd integers is 99. Find the integers.
Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second.
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The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than 8 times the age of the oldest child. Find the ages of the three children.
Practice
1) The sides of a square are altered so that one is increased by 3 and the other is decreased by 1. The area of the new shape is 32 ft2. What was the area of the original square?
2) A right triangle has a longer leg that is 2 unit longer than its shortest leg. Its hypotenuse is 4 units longer than the shortest leg. Using the Pythagorean Theorem, find the dimensions of the original triangle.
3) When the square of a certain number is decreased by 9 times the number the result is 70. Find the number.
4) The product of two consecutive odd integers is 195. Find the integers.
5) The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 5 less than 6 times the age of the oldest child. Find the ages of the three children.