Maximization Using Tables and Graphs California Standards: Algebra 21.0: students graph quadratic functions and know that their roots are the x-intercepts.

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Presentation transcript:

Maximization Using Tables and Graphs California Standards: Algebra 21.0: students graph quadratic functions and know that their roots are the x-intercepts Algebra 23.0: students apply quadratic equations to physical problems

The sum of two numbers is 40. Find the pair, which has the maximum product. First number + second number = 40First number + second number = 40 Identify your variableIdentify your variable First number = xFirst number = x Substitute x for first numberSubstitute x for first number x+second number=40x+second number=40 Solve for second number by subtracting x from both sides of the equationSolve for second number by subtracting x from both sides of the equation Second number = 40-xSecond number = 40-x y is the product that needs to be maximizedy is the product that needs to be maximized y=first number times second numbery=first number times second number y=x(40-x)y=x(40-x)

Graphing

Graphing Calculator TI Press the “Y=” button at the top left corner of the calculator Enter –x^2+40x next to the first Y Press the “graph” button at the top right corner of the calculator In order to view the graph properly, press the “zoom” button at the top of the calculator and scroll down to “zoomfit” and press enter You might want to zoom out if you can’t see the the vertex of the graph. To do this, press “zoom”, scroll down to “zoom out” and press enter. Move your cursor to part of the graph that you would like to focus on and press enter. If you would like to focus on a more specific area, press “zoom”, scroll down to “zoom box” and press enter. Place your cursor where you want the start of your box to be. Press enter. Move the arrow to the right or left and up or down to create your box. Press enter again. To find the vertex, press second (the yellow button) and press trace. Scroll down to either maximum (or minimum if your graph opens up). You will be asked to set the left bound. Place your cursor where you want the left bound to be and press enter. You will then be asked to set the right bound. Move your cursor to the right and press enter. You will be asked if you are ready to guess and press enter. You will now see the value for the vertex.

Questions: Analyze the two strategies and evaluate the effectiveness of each.Analyze the two strategies and evaluate the effectiveness of each. When will you use each strategy?When will you use each strategy?

ASSESSMENT WORK WITH YOUR PARTNER TO CREATE A WORD PROBLEM THAT CAN BE SOLVED USING TABLES AND GRAPHS.WORK WITH YOUR PARTNER TO CREATE A WORD PROBLEM THAT CAN BE SOLVED USING TABLES AND GRAPHS. VOTE ON THE 10 BEST PROBLEMS THAT WILL BE USED ON YOUR FINAL ASSESSMENT.VOTE ON THE 10 BEST PROBLEMS THAT WILL BE USED ON YOUR FINAL ASSESSMENT.