Solving Story Problems with Quadratic Equations

1
Solving Story Problemswith Quadratic Equations
2
Cost and Revenue Problems

• The cost in millions of dollars for a company to
  manufacture x thousand automobiles is given by
  the function C(x) 4x2 - 16x 36. Find the
  number of automobiles that must be produced to
  minimize the cost.
• We know we have a quadratic equation and we are
  asked something about a minimum, so first lets
  find the axis of symmetry.
• The phrase x thousand automobiles tells us that
  x is the variable related to the number of
  automobiles, so the answer is 2,000 automobiles
  must be produced to minimize the cost.
• If theyd asked for the minimum cost, we would
  have had to plug x into the function and solve
  for C(x).

3
Problems Involving Gravity

• A person standing close to the edge on top of a
  304-foot building throws a baseball vertically
  upward. The quadratic function h(t) -16t2 64t
  304 models the ball's height above the ground,
  h(t), in feet, t seconds after it was thrown.
  After how many seconds does the ball reach its
  maximum height? Round to the nearest tenth of a
  second if necessary.
• We know we have a quadratic equation and we are
  asked something about a maximum, so first lets
  find the axis of symmetry.
• The phrase t seconds after it was thrown tells
  us that t is the number of seconds, so the answer
  is The ball will reach its maximum height after
  2 seconds.
• If theyd asked for the maximum height, we would
  have had to plug x into the function and solve
  for h(x).