# SWBAT Using completing the square to put a

- Slides: 16

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Vertex Form When a >1

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form • POW#4 Due Today! • (please put in folder) • 10 Min Give Back Quiz • Work on Warm Up – Day 6 B • First 4 questions

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Do Now: Solve for ‘x’ by Completing the Square: Write in Vertex Form: y = x 2 + 12 x + 32 y = x 2 + 24 x + 145

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Do Now: Solve for ‘x’ by Completing the Square: x 2 - 8 x = -15 +16 + 16 x 2 - 8 x + 16 = 1 (x-4)2 = 1 x = 4± 1 x = 3 and x = 5

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: You Try:

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Do Now: Write in Vertex Form: y = x 2 + 12 x + 32 y = x 2 + 24 x + 145 y - 145 = x 2 + 24 x +144 + 144 y - 1 = x 2 + 24 x + 144 y = (x+12)2 + 1

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: Example 1: y = 2 x 2 + 12 x - 4 • Isolate c y + 4 = 2 x 2 + 12 x y + 4 = 2(x 2 + 6 x + 18 ) • Factor out ‘a’ a=2 + 9 y + 22 = 2(x 2 + 6 x + 9) y = 2(x+3)2 - 22 + 18 2(9)

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: 2 Example 2: y = 3 x - 18 x + 7 y - 7 = 3 x 2 - 18 x y - 7 = 3(x 2 - 6 x + 27 y + 20 = y = + 9 ) 3(x-3)2 2 3(x-3) - 20

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: You Try:

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form : EXAMPLE 3 y = 3 x 2 + 12 x - 14 y + 14 = 3 x 2 + 12 x y + 14 = 3(x 2 + 4 x +12 = ) +4 y + 26 = 3(x 2 + 4 x + 4) y + 26 = 3(x+2)2 y = 3(x+2)2 - 26 Vertex (-2, -26)

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: Example 3 & 4: Example 3: y = 3 x 2 + 12 x - 14 Example 4: y = 5 x 2 - 50 x + 128 y = 5(x-5)2 + 3 (5, 3)

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Write in Vertex Form: Example 5 & 6: Example 5: y = 8 x 2 - 16 x + 27 Example 6: y = 5 x 2 - 40 x + 67 y = 8(x-1)2 + 19 y = 5(x-4)2 – 13 (1, 19) (4, -13)

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form

SWBAT: Review for quiz on complex numbers, imaginary numbers and Vertex form Place in Vertex Form and Identify the Vertex: Simplify the following: i 78

SWBAT: Using completing the square to put a quadratic equation given in standard form into vertex form Place in Vertex Form and Identify the Vertex: y = (x-1)2 -7 ∙ Vertex (1, -7) ∙ Simplify the following: i 78 i 2 = -1 ∙ ∙ ∙

SWBAT: Solving quadratics by completing the square y = x 2 - 2 x - 6 y + 6 = x 2 - 2 x +1 = +1 y + 7 = x 2 - 2 x + 1 y + 7 = (x+1)2 y = (x-4)2 - 7 Vertex (4, -7)

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