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Step-by-step explanation:

Step-by-step explanation:

Standard form:

Vertex form:

Identity used:

6 - 7)

Standard to vertex form conversion by completing the square

y = x² - 3x + 16

  = x² - 2*1*3/2 + (3/2)² - (3/2)² + 16

  = (x - 3/2)² - 9/4 + 16 =

  = (x - 1.5)² + 13.75

8 - 9)

Same as above

y = x² - 2x + 3

  = x² - 2*1*x + 1² - 1² + 3

  = (x - 1)² + 2

10 - 12)

Vertex to standard for conversion by opening parenthesis and simplification

y = (x - 11)² + 15

  = x² - 22x + 121 + 15

  = x² - 22x + 136

13-15)

Same as above

y = (x - 4)² + 11

  = x² - 8x + 16 + 11

  = x² = 8x + 27

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

sine

step-by-step explanation: