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# function

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please find the vertex, the axis of symmetry, determine whether there is a maximum or minimum value and find that value and lastly graphthe function ......of

(I)  f(x)= -x^2-6x+3

Pills  Mar 28, 2017
#1
+87301
+1

f(x) = - x^2  -6x  + 3

The x coordinate of the vertexx =  6 / (2 * -1)   =  -3 To find the y coordinate...put this back into the function   =

- (-3)^2 - 6 (-3)  + 3  =  -9 + 18 + 3  = 12

So the vertex  = ( -3, 12 )

The axis of symmetry  →   x = -3

This parbola turns "upside" down, so the vertex is a max

Graph : https://www.desmos.com/calculator/rzmxqd4pqh

CPhill  Mar 28, 2017
#2
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Thanks @CPhill.....can you please solve it again using the method of completing the square?

Pills  Mar 29, 2017
#3
+87301
+1

f (x)  =  -x^2 -6x  + 3

f (x)  =  -  [ x^2  + 6x - 3 ]    take 1/2 of 6 = 3...square it = 9....add it and subtract it

f(x)  = - [ x^2  + 6x + 9  - 3 - 9 ]   factor the first three terms.....simplify the last two

f(x)   = - [ (x + 3)^2   - 12 ]   apply the negative across the terms

f(x)  = -(x +3)^2  + 12    ....this is vertex form......and the vertex  is  (-3, 12)

The rest  of the problem is the same as before....the negative out front indicates that the parabola is inverted [upside down ]

CPhill  Mar 29, 2017