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WARM-UP

WARM-UP. MULTIPLY:. (x +2)(x + 2) (x - 3)(x – 3) 3. (x + 6)(x + 6) 4. (x – 5)(x – 5) 5. (x + 4) 2. WARM-UP. MULTIPLY:. (x +2)(x + 2) = x 2 + 4x + 4 (x - 3)(x – 3) = x 2 – 6x + 9 3. (x + 6)(x + 6) = x 2 + 12x + 36 4. (x – 5)(x – 5) = x 2 – 10x + 25

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WARM-UP

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  1. WARM-UP MULTIPLY: • (x +2)(x + 2) • (x - 3)(x – 3) • 3. (x + 6)(x + 6) • 4. (x – 5)(x – 5) • 5. (x + 4)2

  2. WARM-UP MULTIPLY: • (x +2)(x + 2) = x2 + 4x + 4 • (x - 3)(x – 3) = x2 – 6x + 9 • 3. (x + 6)(x + 6) = x2 + 12x + 36 • 4. (x – 5)(x – 5) = x2 – 10x + 25 • 5. (x + 4)2 = x2 + 8x + 16

  3. Converting from Vertex Form to Standard Form • Square the binomial. • Distribute. • 3. Combine like terms. • 4. Simplify.

  4. Converting from Vertex Form to Standard Form • Ex: y=3(x-1)2+8 =3(x-1)(x-1)+8 =3(x2-x-x+1)+8 =3(x2-2x+1)+8 =3x2-6x+3+8 y=3x2-6x+11

  5. Converting from Vertex Form to Standard Form • Convert y = 3(x + 1)2 – 5 • Convert y = 2(x - 4)2 - 1 Standard form: y = 3x2 + 6x - 2 Standard form: y = 2x2 – 16x = 31

  6. Converting to Standard Form from Vertex Form • Use to find the vertex, (h, k). • Use the a from the standard form equation. • 3. Substitute a, h, and k into y = a (x-h)2 + k.

  7. Converting from Standard Form to Vertex Form • Ex: y= -3x2 – 12x - 13 y = -3(-2)2 – 12(-2) – 13 y = -12 + 24 -13 y = -1 Vertex (-2, -1) a = -3 y = a(x – h)2 + k y = -3(x – (-2))2 -1 y = -3(x + 2)2 – 1

  8. Converting from Standard Form to Vertex Form • Convert y = 2x2 – 4x + 5 • Convert y = -x2 – 2x + 1 Vertex = (1, 3) a = 2 Vertex form: y = 2(x-1)2 + 3 Vertex = (-1, 2) a = -1 Vertex form: y = -(x+1)2 + 2

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