Application of Quadratic Equations

Examples, solutions, videos, worksheets, games and activities to help Algebra 1 students learn how to solve word problems that involve quadratic equations.

Applications of Quadratic Equations - Quadratic Equation Word Problems, part 1
How to approach word problems that involve quadratic equations?
Solving word problems with quadratic equations - consecutive integer and rectangle dimensions problems.
Examples:

1. The product of two consecutive integers is 5 more than three times the larger. Find the integers.
   
2. The width of a rectangle is 5 feet less than its length. Find the dimensions of the rectangle if the area is 84 square feet.

Applications of Quadratic Equations - Quadratic Equation Word Problems, part 2
How to approach word problems that involve quadratic equations.
Solving projectile problems with quadratic equations.
Example:
A projectile is launched from a tower into the air with an initial velocity of 48 feet per second. Its height, h, in feet, above the ground is modeled by the function
h = -16t² + v₀t + 64
where t is the time, in seconds, since the projectile was launched and v₀ is the initial velocity.
How long was the projectile in the air?
When did it reach its maximum height?

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Application Of Quadratic Equations
Example:
The height of a triangle is 4 times its base. The area of the triangle is 288cm². Find the base and length of the triangle.

Learn how to solve application involving quadratic equations.
Examples:

1. One leg of a right triangle is 2 feet longer than the shorter side. If the length of the hypotenuse is 18 feet. How long is each leg?
   
2. Find the area of a right triangle with sides x, x+7 and x+8 inches.
   
3. If the height of a ball t seconds after it is thrown vertically upwards is given by h = 64t - 16t², find when the ball will be
   a) 48 ft
   b) back on the ground.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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