Solving Quadratic Equations Word Problems

Use whatever method you think is best for each problem: quadratic formula, graphing calculator, graphing by hand or factoring.

Sketch a graph or diagram for quadratic problem labeling the important data points. Remember that the x and y axis must ALWAYS be labeled.

  1. You and your friend are building rockets in science class. There is a competition to see whose rocket will go the highest. Your rocket’s height, in feet, can be described by the equation g(x) = -16x2 + 180x while your friend’s is represented by f(x) = -16x2 + 240x
  2. Who wins?
  3. What is the max height for each rocket?
  4. How long does it take each rocket to hit the ground?
  1. At a swim meet, Janet dives from a diving board. Her position above the water is represented by the equation h(t) = -16t2 + 24t + 40.
  2. After how many seconds does Janet enter the water?
  3. What is the greatest height Janet reaches in her dive?
  4. How long does it take to reach the maximum height?
  5. How long into her dive is she at 24 feet from the water?
  1. You built a pirate ship prop for the Pope High School Marching Band to take to competition. Your ship is a triangular shapethat is 10 feet wide at its widest point and 40 feet tall at its tallest point. (Ignore the fact that this wouldn’t float well, we are staying on land after all!) You find out that the entrance to the Vanderbilt athletic field is a parabolic archway. This archway is modeled by the equation d = 12x – x2, where d represents the distance, in feet, that the arch is above the ground (the height) for an x value. The band director came to you asking if you will be able to get the ship onto the field. What do you tell him? Why?
  2. The profits of Mr. Unlucky’s company can be represented by the equation y = -3x2 + 18x – 4, where y is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell before he ends up in debt.
  3. When will Mr. Unlucky’s business show the maximum profit?
  4. What is his maximum profit?
  5. When will he start losing money?
  6. When will he be no longer making any money?
  1. Astronauts working on a space station on the moon toss a ball into the air. The height of the ball is represented by the equation f(t) = -2.7t2 + 13.5t + 14, where t represents time in seconds since the ball was thrown and f(t) represents the height of the ball in feet.
  2. To the nearest hundredth of a second, after how much time does the ball hit the ground?
  3. To the nearest tenth of a foot, what is the greatest height the ball achieves?
  1. You throw a ball upward from a height of 15 feet with an initial upward velocity of 5 ft/s. The path of the ball can be modeled by the equation h(t) = -16t2 + 5t + 15
  2. What is the maximum height of the ball?
  3. What is the height of the ball at 2 seconds?
  4. How long does it take to reach the maximum height?
  5. How long does it take for the ball to reach the ground?
  1. Mr. Jackson had a rectangular garden where the length is 2 less than twice the width. If the area of the garden is 420 square feet, find the dimensions of the garden.

Sketch: (graph, diagram, or picture) / Answers:
Sketch: (graph, diagram, or picture) / Answers: