Quadratic Applications Practice Problems

Here you will find a concise collection of quadratic applications practice problems. Visit this page directly at hunkim.com/quadraticapplications

  1. Height (in metres) is a function of time (in seconds). On planet Z, h(t)=-(t-2)^2+10 models your height jumping off a cliff into water.
    1. What is your initial height?
    2. When do you reach your maximum height?
    3. What is the maximum height that you achieve?
    4. After you jump, for how long are you above the height of 6 metres?
    5. When do you land in the water?

  2. You have 250 m of fencing. Find the maximum possible rectangular area.

  3. You have 1000 feet to fence off your plot of land which is adjacent to a lake. Fencing is only used on three sides of your rectangular property because of the water.
    1. What dimensions should be used to maximize the area of your land?
    2. What is the minimum possible area?

  4. See diagram below:

    You have 1200 m of fencing to enclose two adjacent rectangular regions of equal lengths and widths as shown in the diagram below. What is the maximum area that can be enclosed by the fencing?

  5. You sell 3000 phone cases each month at a price of $20 each. For each $1 price increase, you sell 100 less phone cases.
    1. What price should you set to maximize revenue?
    2. What is the maximum revenue?
    3. How many phone cases are sold when revenue is maximized?

  6. You have 300 m of fencing.  Find  and  to maximize the area of the yard.


  7. The shortest cable in the bridge below is a=10 m. Find length b.


  8. Two cars are travelling along two straight roads which are perpendicular to each other and meet at the point O, as shown in the diagram.  The first car starts 20 km west of O and travels east at a constant speed of 10 kph.  The second car starts 50 km north of O at the same time and travels south at a constant speed of 5 kph. 
    1. Write a formula that expresses the relationship between the distance between the two cars.  There is no need to do any algebra.

    2. Use desmos.com find find out when the distance between these cars are minimized.