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quadratic equations
completing the square
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Quadratic Equations
These problems involve the use of a quadratic equation. In most cases the quadratic equation must be solved, but in some problems the equation may be used only for modeling and to make predictions.

Problems that deal more generally with polynomials can be found in the Polynomials category.

Some of these problems are also in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Algebra: Quadratic Equations
The closest match in our Ask Dr. Math archives:
   Quadratic Equations
NCTM Standards:
   Algebra Standard for Grades 9-12

Access to these problems requires a Membership.

All Wet - Linda Benton
Algebra, difficulty level 3. Solve simultaneous equations, find area, and use the Pythagorean theorem and percentages to find the spraying distance needed for a circular sprinkler in a rectangular yard. ... more>>

The Chip Swap Game - Ethel Breuche
Algebra, difficulty level 4. The object of this game is to swap the positions of the different colored chips. Count the number of moves and, as you increase the number of chips, find the general formula. ... more>>

The Christmas Gifts - Terry Trotter
Algebra, difficulty level 2. A grandfather doles out his annual Christmas gifts to his beloved grandchildren in a most unusual way - mathematical, of course. ... more>>

The Continued Fraction - Ethel Breuche
Algebra, difficulty level 4. Find the value of a given continued fraction. ... more>>

Elbert's Equation - Steve Risberg
Algebra, difficulty level 3. Use exponent properties, absolute value, and quadratic equations to find the six solutions to Elbert's equation. ... more>>

An Expanding Circle - Steve Risberg
Algebra, difficulty level 2. When the radius of a circle increases by 6 inches, the area increases by 125%. Find the original radius. ... more>>

The Length of Larry's Rectangle - Larry Sue
Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him? ... more>>

Lost in Mathland - Steve Risberg
Algebra, difficulty level 2. Zach and Zeke get separated while hiking in Mathland, where roads are named with equations. Zeke is at the intersection of three roads - can you help Zach determine where he is? ... more>>

Making Triangles - Steve Risberg
Algebra, difficulty level 4. The lengths of three segments are represented by (n + 2)^2, 9, and n(n + 5). Determine for what values of 'n' these three segments can be used to form a triangle. ... more>>

Many or Money? - Steve Risberg
Algebra, difficulty level 3. Help the Student Council decide how much to charge for tickets to the concert. ... more>>

Maxwell's Mowing - Terry Trotter
Algebra, difficulty level 1. Maxwell mows rectangular lawns by mowing around the rectangle, leaving a smaller rectangle. If the lawn is 200 feet by 120 feet, how wide a swath has he mowed so far if his mower runs out of gas 1/4 of the way through? ... more>>

Poolish Pride? - Steve Risberg
Algebra, difficulty level 3. Two competitive brothers build rectangular pools of similar shape but different size. Given some information relating the lengths and widths, find the area of the larger pool. ... more>>

Radical Rectangle - Steve Risberg
Algebra, difficulty level 2. Solve a quadratic equation to find the area of a rectangle, expressing your answer in simplified radical form. ... more>>

Reciprocals - Steve Risberg
Algebra, difficulty level 3. Explore the numeric difference between numbers and their reciprocals. ... more>>

Rocket Science - Steve Risberg
Algebra, difficulty level 1. Given the initial velocity of a model rocket, determine at what time the rocket attains a certain height. ... more>>

Throw It Down! - Steve Risberg
Algebra, difficulty level 3. Kelvin leaps high to dunk a basketball. How long are his hands high enough above the rim for him to dunk? ... more>>

Valentine Candy - Ethel Breuche
Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twenty-five-cent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit? ... more>>

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