Applications of quadratic functions

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  1. Different Ways to Solve Quadratic Functions
  1. A farmer wants to build a rectangular pig farm beside a river. He has 200 meters of fencing material, and there is no need for fencing on the side along the river. What are the dimensions of the largest pig farm this farmer can build?
    1. The sum of two integers is 10, and the product is a maximum. Find the integers.
      1. The sum of two integers is 10, and the sum of their squares is a minimum. Find the integers.
        1. John stands on the roof of a building and throws a ball upwards. The ball's height above the ground is given by the formula: h=−3t2+12t+15h = - 3{t^2} + 12t + 15, where h is the height in meters at t seconds after the ball is thrown.
          1. How high is John above the ground when he throws the ball?
          2. Find the height above the ground of the ball 1 second after the ball is thrown.
          3. How long does it take for the ball to reach the maximum height?
          4. Find the maximum height above the ground reached by the ball.
          5. How long does it take for the ball to hit the ground?
        2. A school Halloween dance charges $5 for admission, and 200 students are willing to attend the dance. For every 25 cents increase in price, attendance drops by 4 students.
          1. What price should the school charge to maximize the revenue?
          2. How many students would need to attend the dance in order to generate the maximum revenue?
          3. What is the maximum revenue?