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The instructions said: TEAM QUIZ Use what you learned yesterday about the graphing form of quadratic equations to sketch the graphs of these parabolas without using your graphing calculators. On Friday morning the substitute arrived late, and the custodian let the first period Algebra I class into the room. Several eager students saw the assignment on the board and thought it was for them. They immediately went to the board and started doing the one thing they had learned so far, multiplying out the squared expression and simplifying. They had just finished replacing the last equations with its simplified form when the substitute arrived with a completely different assignment for them. When the students in the fourth period Algebra 2 class arrived, they read the instructions and saw the list of equations, all in standard form. The first one was:  EMBED Equation.3 . Making the xy-tables and plotting point-by-point would take forever. They had to find another way. Enrico said, We need that other form of the equation that tells us the vertex. How do we get that? Jessica suggested, We know how to get the coordinates of the x-intercepts. What are the coordinates of the x-intercepts for this equation? Kevin said, And parabolas are symmetric, so the vertex is mid-way between them. How could you find the x-value of the vertex? Find it. Kenya volunteered, And if we know the x-value, we can find the y-value that goes with it. Find the y-value. Weve got the vertex. Now we can make a sketch! the all said together. Make a sketch of this function, label the intercepts and the vertex, and draw in a line of symmetry. How can we be sure were right? asked Jessica. Couldnt we write the graphing form of the equation then work it out to see if we get the original one in standard form? Enrico suggested. Use the vertex to write the equation in graphing form. Show your work to verify that it is the same as the original by squaring and simplifying. The following four functions were also part of Ms. Speedis Quiz. For each function do parts (1) through (5) as in the previous problem in order to write and verify the graphing form:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 . On Friday afternoon the custodian erased all the boards, so when Ms. Speedi returned on Monday, she assumed her Algebra 2 students had just started with the graphing forms. She never realized that her class had figured out their own method for changing the equation from standard form to graphing form. Based on your work with the two preceding problems, describe the students method for finding the vertex without drawing the graph and for figuring out the graphing form of the equation of a parabola from the standard form. With your team, make up another example, and show how to use the method you described. Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. 1.  EMBED Equation.3  2.  EMBED Equation.3  3.  EMBED Equation.3  4.  EMBED Equation.3  Did you need to average the x-intercepts to find the vertex in part (4) of the preceding problem? 1. What are the coordinates of the vertex in part (4)? 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