Solving Story Problems with Quadratic Equations

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) = 4x x 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 let’s 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 they’d asked for the minimum cost, we would have had to plug x into the function and solve for C(x).

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) = -16t t +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 let’s 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 they’d asked for the maximum height, we would have had to plug x into the function and solve for h(x).