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