1. College Algebra Chapter 1 Equations and Inequalities
Section 1.5
Applications of Quadratic Equations
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2. Concepts Solve Applications Involving Quadratic Equations and Geometry
Solve Applications Involving Quadratic Models

3. Concept 1 Solve Applications Involving Quadratic Equations and Geometry

4. Example 1 (1 of 2)
Dmitri is having a fish tank constructed to fit in a niche in his wall. The width must be 12 inches, while the length is twice the height decreased by 8 inches. The total volume of the tank must be 6840 cubic inches. What are the dimensions of the tank?

5. Example 1 (2 of 2)
If 1 gallon of water measures 231 cubic inches and weighs pounds, what will be the weight of the water in the tank?

6. Skill Practice 1
A box is to be formed by taking a sheet of cardboard and cutting away four 2 in. by 2 in. squares from each corner. Then the sides are turned up to form a box that holds 56 in.3 If the length of the original piece of cardboard is 3 in. more than the width. find the dimensions of the original sheet of cardboard.

7. Example 2
The three sides of a right triangle are represented by three consecutive integers. What are the integers?

8. Example 3
As the minute hand on the face of a clock sweeps around once, it covers an area of 114 square inches. What is the length of the minute hand? Round your answer to the nearest inch.

9. Example 4
Morris is designing a new sign for his ice cream shop to be placed by the exit from a nearby highway. The sign needs to be big. Really big. He plans on making the height of the bottom triangle 3 times the height of the semicircle on top and having a total area of 74 square feet. If the county will not allow any signage taller than 15 feet, will Morris be allowed to put up his cone? Use π = 3.14 and round your answer to the nearest foot.

10. Example 5 (1 of 3)
Quilters can create an astonishing variety of patterns using basic geometric shapes. The card trick quilt pattern is built from squares, half-triangles, and quarter-triangles. The finished pattern looks like overlapping "cards."

11. Example 5 (2 of 3)
If each small square measures 3 inches by 3 inches, what is the length of the full diagonal of the 9 square pattern to the right?

12. Example 5 (3 of 3)
Anne Marie is making a quilt from 9 inch square card trick blocks. The quilt will be 2 blocks wide, 3 blocks long and have a border of width x all the way around. What should the width of the border be so Anne Marie's quilt measures 682 square inches?

13. Skill Practice 2
A sail on a sailboat is in the shape of two adjacent right triangles. The hypotenuse of the lower triangle is 10 ft, and one leg is 2 ft shorter than the other leg. Find the lengths of the legs of the lower triangle.

14. Concept 2 Solve Applications Involving Quadratic Models

15. Example 6
The average weekly earnings E in dollars, for a group of workers can be approximated by
where x represents the number of years since 2004.
Determine the average weekly earnings in 2007.
In what year will the average weekly earnings reach $638?

16. Solve Applications Involving Quadratic Models
If an object has an initial vertical position and initial velocity straight upward or downward, then the vertical position s of the object is given by

17. Example 7
An arrow is shot from a height of 6 feet straight upward with an initial speed of 20ft/sec.
Write a model to express the arrow's height (in feet) above the ground after t seconds
How long will it take the arrow to land?

18. Skill Practice 3
A fireworks mortar is launched straight upward from a pool deck 2 m off the ground at an initial velocity of 40 m/sec.
Write a model to express the height of the mortar is (in meters) above ground level.
Find the time(s) at which the mortar is at a height of 60 m. Round to 1 decimal place.
Find the time(s) at which the rocket is at a height of 100 m.