Question 1048459
y = 3x^2 + 15x + 9 
:
y - 9 = 3x^2 + 15x
:
y - 9 = 3(x^2 +5x)
:
y - 9 + 3(25/4) = 3(x^2 +5x + 25/4)
:
y - 36/4 + 75/4 = 3(x + 5/2)^2
:
y + 39/4 = 3(x + 5/2)^2
:
y = 3(x + 5/2)^2 - 39/4
:
y = 3( x - (-5/2))^2 - 39/4
:
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vertex is at (-5/2, -39/4) which is a minimum
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:
we can check this by using
:
x = -b/2a = -15 / 6 = -5/2
:
y = 3(-5/2)^2 + 15(-5/2) + 9 
:
y = 75/4 -150/4 + 36/4 = -39/4
:
our answer (-5/2, -39/4) checks
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