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# Class Note for MATH 1330 with Professor Flagg at UH

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15

PreCalSection2 4 Example 1 If the sum of two numbers is 14 nd the largest possible value of their product Example 2 A farmer has 1500 feet of fencing He wants to fence off a rectangular field that borders a straight river needing no fence along the river What are the dimensions of the field that has the largest area PreCalSection2 4 Example 3 The hypotenuse of a right triangle is 6 m Express the area A of the triangle as a function of the length x of one of the legs Example 4 The area of a rectangle is 36 square feet Express its perimeter P as a function of its width w Example 5 A rectangle has a base on the xaxis and its upper two vertices on the parabola y 9 x2 Express the area A of the rectangle as a function of x Express the perimeter P of the rectangle as a function of x PreCalSectionZ 4 Example 6 A wire of length x is bent into the shape of a rectangle with the length of the rectangle twice its width Express the area A of the rectangle as a function of x Example 7 Let Pxy be a point on the graph of y x2 10 Express the distance d from P to the point 02 as a function of x Example 8 A square is inscribed in a circle of radius 4 cm Express the perimeter P of the rectangle in terms of its width w PreCalSection2 4 Math 1330 Section 24 Applications WORD PROBLEMS How to Set Up and Solve Word Problems with Quadratic Functions 1 Read the question and identify speci cally what function is either asked for or needed to nd the optimal solution Write down what is given in an organized way Write down the geometric formulas used if applicable Use the information you have to write the function in terms of one variable To solve a quadratic for an optimal value of x use the vertex Remember that the function has a minimum at the vertex if the parabola opens up and a maximum at the vertex if the parabola opens down 6 We can use the formula for the vertex if our quadratic function is fx axz bx c then the vertex is the point b b Za Z Elk59 Example The perimeter of a rectangle is 54 feet a Express its area A as a function of the width w Call w the width of the rectangle Call 1 the length of the rectangle Then we know the equation for the perimeter is P 21 2w Using the fact that we know the perimeter is 54 we can solve the perimeter P 2w 54 2w 2 equation for l in terms of w which gives 1 27 w Area of a rectangle equals length times width so A wl w27 w 27w w2 b For what value of w is A the greatest A w2 27w which is a quadratic and its graph is a parabola opening down The greatest value of A will be the y value of the vertex Using the formula for the vertex it occurs when w i 22 7 c What is the maximum area of the rectangle To find the maximum area find A Z 2722 7

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