# The graph below illustrates the area of a room in a

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The graph below illustrates the area of a room in a newly remodeled house. The “smaller” parabola was the original size, and the “larger” one represents the new size. Write the function of each parabola as a transformation of the function 2( )f xx. Next, write the function for the larger size as a transformation of the function of the original size. Function of Old Room:Function of New Room:Function of Old to New: Classwork: Mail merge!Page 3 of 18
1.Yesterday we looked at quadratics in _________________ form. Ex: 2312yxa.This is convenient because we can easily identify the vertex: and the “stretch.”2.However, sometimes quadratics are written in ____________________ form: 3.To review “FOIL,” let’s convert 2312yxinto standard form.4.From this form, we still want to be able to find the vertex (and other things)…Standard Form: 2yaxbxcPropertyExample: 222yxx a positivea negativeMax or Min?VertexAxis of Symmetryy-intercept5.How to graph2( )22f xxx Step 1: Plot the _________________Step 2: Sketch the axis of symmetry.Step 3: Plot the _________________Step 4: Use symmetry to find __________Step 5: Sketch!Page 4 of 18U4 D2: Graphing from Standard Form & Identifying the Vertex
1) 2( )321f xxxDirection: _________________Axis of Symmetry: _____________Vertex: _______________Max or Min (and value): _________& __________y-intercept: ___________2) 2( )242f xxx Direction: _________________Axis of Symmetry: _____________Vertex: _______________Max or Min (and value): _________& __________y-intercept: ___________WoRd:A record label uses the function 2908100a ttt to model the sales of a new release. The number of albums sold is a function of time, t, in days. On which day were the most albums sold? What is the maximum number of albums sold on that day?
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1.To start class yesterday, we converted the vertex form into standard form…232yx2.What if we had to work backwards? 21013yxx. This is known as ________________________ the square.2______10______13yxxFill the blanks with _______________Vertex is: _________________3.One more together: This time there is a number front of 2x( 1a). Factor it out!!2( )3615f xxxFactor: Add & Subtract: ___________Vertex: ________________Check: Page 6 of 18U4 D3: Completing the Square: Change from Standard toVertex
Classwork Problems: Directions: Fill in the blank for each expression in order to complete the square.1) 24______xx