### About Applications of Quadratic Equations:

We will often encounter word problems that involve quadratic equations. These problems normally involve the Pythagorean formula, the area of a rectangle given a larger area and a strip of uniform width that surrounds the rectangle, or the height of an object that is propelled directly upward.

Test Objectives

- Demonstrate an understanding of how to set up and solve a word problem
- Demonstrate the ability to solve a word problem that involves the Pythagorean formula
- Demonstrate the ability to solve a word problem that involves the area of a rectangle
- Demonstrate the ability to solve a word problem that involves the height of a propelled object

#1:

Instructions: solve each word problem.

a) Larry needs to wash a window in a building that is 8 feet from the ground. To avoid a fence, he decides to rest the ladder against the building. For stability, Larry decides he should place the ladder 6 feet away from the building. How long of a ladder will Larry need?

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#2:

Instructions: solve each word problem.

a) Two cars left an intersection at the same time. One of the cars traveled directly north, while the other car traveled directly east. Some time later, they ended up being exactly 203 miles apart from each other. If the car that traveled north traveled 7 miles less than the car that traveled east, how far did each car travel?

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#3:

Instructions: solve each word problem.

a) Jamie wants to buy a rug for a room that measures 18 feet wide by 22 feet long. Jamie wants to leave a uniform strip (width is the same) of uncovered floor around the rug. After visiting the carpet store, she buys a rug with an area of 252 square feet. What are the dimensions of the rug?

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#4:

Instructions: solve each word problem.

a) Molly’s backyard is perfectly square and has a total area of 800 square feet. Molly sets up a sprinkler in the very center of her backyard, which sprays water in a circular pattern and only covers her backyard. What is the radius of the circle formed by the water pattern of the sprinkler? (Hint: Draw a picture of the backyard (square) and a circle that touches the four corners of the backyard. Then think about how we can get the distance from one point of the circle to another (this gives us the diameter of the circle). Half of that distance is the radius.)

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#5:

Instructions: solve each word problem.

a) A toy spaceship is launched vertically upward from an initial height of 84 feet. The initial velocity is 20 feet per second. Find out how long before the rocket will hit the ground.

Note: For this problem, we will disregard air resistance

Note: We will use the formula: $$h=-16t^2 + v_0 t + s_0$$ v_{0} is the initial velocity in feet per second

s_{0} is the initial height in feet the projectile is launched from t is the number of seconds

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Written Solutions:

#1:

Solutions:

a) 10 feet

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#2:

Solutions:

a) 140 miles, 147 miles

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#3:

Solutions:

a) 14 feet wide by 18 feet long

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#4:

Solutions:

a) 20 feet

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#5:

Solutions:

a) 3 seconds