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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 912
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.
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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.
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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.
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The Continued Fraction
 Ethel Breuche

Algebra, difficulty level 4. Find the value of a given continued fraction.
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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.
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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.
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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?
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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?
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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.
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Many or Money?
 Steve Risberg

Algebra, difficulty level 3. Help the Student Council decide how much to charge for tickets to the concert.
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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?
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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.
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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.
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Reciprocals
 Steve Risberg

Algebra, difficulty level 3. Explore the numeric difference between numbers and their reciprocals.
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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.
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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?
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Valentine Candy
 Ethel Breuche

Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twentyfivecent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit?
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