Asked by daylan
Write the functions in vertex form with a vertex (-3, -6) and passes through (0, 4.5).
Answers
Answered by
Bosnian
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
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
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