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Warm UP Domain All real numbers Range y -6 Equation y = x ² - 6 Interval of Increase 0 x

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Quadratic Form to Form Notes

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Change quadratic functions to standard form Rewrite (x+1)² Multiply using FOIL Combine like terms Dont forget your +2 Standard Form

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Compare Vertex vs. Standard Vertex form: Standard form: a = 1 b = 2 c = 3 You will learn that you will need to identify the values for a, b, and c. Lets get into the habit of identifying them NOW!! a = 1 h = -1 k = 2 Lets look at our last problem We converted to Compare values

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Lets try this one! Write the quadratic function in standard form. Label the values for a, b, and c. Steps: Write (x+3) twice Multiply using Foil Distribute the negative Add the 1 and combine like terms. Y=-(x+3)(x+3) + 1 Y = -(x ² +6x +9) +1 Y= -x ² -6x Y = -x ² -6x -8

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Your Turn Write the quadratic function in standard form. Label the values for a, b, and c. Steps: Write ( ) twice Mulitply using Foil Distribute number out front Combine like terms.

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Standard to Vertex Step 2: Plug x back into equation to get y value Step 3: change the value of your x Step 1: Find x value Step 4: a from standard form is the same a in vertex form Vertex: (-2, -4)

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Steps Change to standard form 1. FOIL out the ( ) 2. Collect like terms Make sure equation is in y = ax ² +bx + c Y = -2(x-2)(x+3) 3. Distribute Y = -2 (x ² +3x -2x -6) Y = -2(x ² +1x – 6) Y = -2x ² -2x +12

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CLASSWORK/HOMEWORK page 66 (25-27) Problems on Agenda

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Practice Change into Standard form Y = 2(x-4) ² + 5 Form? Vertex (4, 5) FOIL y = 2(x-4)(x-4) y = 2(x ² -4x -4x + 16) Collect like terms y = 2(x² -8x + 16) Distribute y = 2x² - 16x + 32

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Practice Change into standard form Y = 2(x-3)(x+4) Form? Intercept x = 3 x=-4 FOIL y = 2(x ² +4x -3x -12) Collect like terms y= 2(x² + 1x -12) Distribute y = 2x² + 2x -24

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