Check out these 3 great word problems involving quadratic equations in this lesson.
Problem #1: The quadratic equation for the cost in dollars of producing automobile tires is given below where x is the number of tires the company produces. Find the number of tires that will minimize the cost.C = 0.00002x2 - 0.04x + 38
The standard form of a quadratic equation is ax² + bx + c. To solve this problem, we just need 2 important concepts about quadratic equations. First, when we are trying to maximize or minimize, we need to use the formula below that will help us find the x-coordinate of the vertex. Second, if a > 0, the vertex is a minimum. if a < 0, the vertex is a maximum.
Since a = 0.00002 and 0.00002 is bigger than 0, the quadratic equation will give a minimum.
Problem #2: You want to frame a collage of pictures with a 9-ft strip of wood. What dimensions will help you maximize the area?
First, we need to find the quadratic equation.
Area = l × w Perimeter = 2l + 2w
9 = 2l + 2w. Solve for l and replace l in the formula for the area.
9 - 2w = 2l
Problem #3: The sum of two numbers is 12 and their product is 35. What are the two numbers?
Let n and m be the two numbers.
n + m = 12 (1)
n × m = 35 (2)
Using (1), n = 12 - m
(12 - m) × m = 3512m - m2 = 35