Quadratic Word Problems

1. Mr. Lumen replaced a square window with a rectangular one. The new window is 3 ft wider and 2 ft higher than the square one. It has an area of 30 square feet. How long was a side of the original square window?

  • Hint: x = side length of the square
  • You will be setting up a factored quadratic equation
  • You will need to expand it out, then, set it = to 0
  • Finally, factor the new quadratic equation and solve for x!


2. The dimensions of a rectangular garden were 5m by 12m. Each dimension was increased by the same amount. The garden then had an area of 120 square meters. Find the dimensions of the new garden.

  • Hint: x = amount each side was extended by
  • You will have two binomials (each one represents one side of the rectangle) set = to total area
  • Remember: in order to solve the quadratic, you must have it set = to zero.
  • (In order to set this equal to zero, you must expand it out first!)


3. A diver springs from the edge of a cliff 80 ft above the ocean with an initial upward velocity of 8ft/sec. How long will it take the diver to reach the water?

  • Use: h = -16t^2 + vt + c
  • h = approximate height of an object propelled upward (in feet)
  • t = time in motion (in seconds)
  • v = initial upward velocity (in feet per second)
  • c = initial height (in feet)


  • Plug in each value based off the information given in the question.
  • If you are looking for how long it will take the diver to reach the water, what variable are you looking for?
  • If the diver is reaching the water, his height will be.....?


4. At a pep rally, cheerleaders use a slingshot to launch small, foam basketballs into the crowd. The release point is 5ft above the gym floor, and the balls are shot with an inital upward velocity of 36ft/sec. Suppose a ball is caught 13 ft above the floor on its way down by a student in the stands. How long is the ball in the air?

  • Use the same formula as #3, but plug in the values that represent this question.
  • If you are looking for how long the ball is in the air, what variable are you looking to find?