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**Warm UP Domain All real numbers Range y ≥ -6 Equation y = x² - 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 Don’t forget your +2 Combine like terms Standard Form

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**Compare Vertex vs. Standard**

Standard form: Vertex form: Lets look at our last problem We converted to a = 1 b = 2 c = 3 a = 1 h = -1 k = 2 Compare values 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!!

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**Lets try this one! Y = -x² -6x -8**

Write the quadratic function in standard form. Label the values for a, b, and c. Y=-(x+3)(x+3) + 1 Steps: Write (x+3) twice Multiply using Foil Distribute the negative Add the 1 and combine like terms. Y = -(x² +6x +9) +1 Y= -x² -6x -9 +1 Y = -x² -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 a x y Step 1: Find x value**

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

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**Intercept Form Change to standard form Y = -2(x-2)(x+3) Steps**

1. FOIL out the ( ) Y = -2 (x² +3x -2x -6) 2. Collect like terms Y = -2(x² +1x – 6) 3. Distribute Y = -2x² -2x +12 Make sure equation is in y = ax² +bx + c

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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(x² -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(x² +4x -3x -12) Collect like terms y= 2(x² + 1x -12) Distribute y = 2x² + 2x -24

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Quadratic Equations and Complex Numbers

Quadratic Equations and Complex Numbers

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