Write the functions in vertex form with a vertex (-3, -6) and passes through (0, 4.5).

Answer 1

The vertex form of a quadratic function:

y = a ( x - h )² + k

In this case:

horizontal shift :

h = - 3

vertical shift :

k = - 6

y = a ( x - h )² + k

y = a [ x - ( - 3 ) ] ² + ( - 6 )

y = a ( x + 3 ) ² - 6

For x = 0 , y = 4.5

y = a ( x + 3 ) ² - 6

4.5 = a ( 0 + 3 ) ² - 6

4.5 = 9 a - 6

Add 6 to both sides

10.5 = 9 a

a = 10.5 / 9 = 105 / 90 = 3 ∙ 35 / 3 ∙ 30 = 35 / 30

y = 35 / 30 ( x + 3 ) ² - 6