Consecutive Integers: Quadratics and Word Problems in Math

1. The product of two consecutive integers is 72. What are the integers? Graph the quadratic function that represents this situation.

• 6 and 7

• The integers are 8 and 9.

• 9 and 10

• 7 and 8

2. A rectangle's length is one more than its width. If the area of the rectangle is 30 square units, find the dimensions and graph the quadratic equation.

• Width: 3 units, Length: 4 units

• Width: 5 units, Length: 6 units

• Width: 6 units, Length: 7 units

• Width: 4 units, Length: 5 units

3. The product of three consecutive integers is 120. What are the integers? Write a quadratic equation to represent the product of the first two integers and graph it.

• 2, 3, and 4

• 5, 6, and 7

• The integers are 4, 5, and 6.

• 3, 4, and 5

4. If the sum of two consecutive integers is 25, what are the integers? Create a quadratic equation and graph it to visualize the solution.

• 12 and 13

• 8 and 9

• 10 and 11

• 14 and 15

5. A farmer has a rectangular field where the length is twice the width. If the area is 50 square meters, find the dimensions and graph the quadratic function.

• Width: 6 meters, Length: 12 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

6. The product of two consecutive integers is equal to the square of the first integer. What are the integers? Graph the quadratic equation that represents this relationship.

• 1 and 2

• 2 and 3

• 0 and 1

• -1 and 0

7. A number and its consecutive integer have a product of 56. What are the two integers? Write the quadratic equation and graph it.

• The two integers are 7 and 8.

• 8 and 9

• 5 and 6

• 6 and 7

9. The sum of two consecutive integers is 17. What are the integers? Formulate a quadratic equation and graph it to show the solution.

• 8 and 9

• 7 and 8

• 6 and 7

• 10 and 11

10. A number and the next consecutive integer have a product of 42. Determine the integers and graph the quadratic equation that represents this scenario.

• -5 and -4

• The integers are 6 and 7, or -7 and -6.

• 5 and 8

• 3 and 4