Real-World Quadratic FunctionsCarlton Hunter
MAT 222 Week 5 Assignment
Instructor Andrea Grych
October 27, 2014
Real-World Quadratic FunctionsQuadratic Functions are more than mathematical notations because they are widely used in science, medicine, and engineering. The U-shape of a parabola can be used to incorporate into structures like the parabolic reflectors that form the base of satellite dishes and car headlights. Quadratic Functions has help forecast business profit and loss, and even assist in determining the minimum and maximum values. Most of the objects we use every day, from cars to buildings, would not exist if quadratic functions weren’t applied to their designs. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit? (Dugopolski, 2012) This is the problem we will be solving for this assignment. P=-25x2+300xProfit Function
0=-25x2+300xTurn the function into a Quadratic equation
0=25x2+300xDivided both sides by -1
0=25x(x-12)We factored the right side and now we can use the Zero Factor Property 25x=0 or x-12=0Solve each equation
x=0 or x=12the parabola will cross the x-axis at 0 and x = 0 or x = 12 the parabola will cross the x-axis at 0 & 12. Since the quadratic function has a large value the parabola will most likely be narrowed. The parabola will also have a negative value so it will be open downward; in addition to that the maximum value of the graphed parabola will be at the vertex. Now we will be finding out what number of clerks will maximize the profit. -b(2a)
-3002(-25) Values are now negative because of the negative within the formula. -30050 We can now simplify
x=6 There will be a total of 6 clerks working that will maximize profit. Finally we will be finding out what is the maximum possible profit when this...
References: Dugopolski, M. (2012). Elementary and intermediate algebra (4th Ed.). New York, NY: McGraw-Hill Publishing.
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