What is the the vertex of #y =-x^2-3x-6 #?

Answer 1

Hazel Anglin

#(-3/2,-3/2)#

#(-b)/(2a)# is the #x# coordinate at this point

#(--3)/(2xx-1)# =#3/(-2)#

Put this value into the equation to find the #y# value

#(-3/(-2))^2-3xx(3/(-2))-6#

= #9/4+9/4-6#= #18/4-6#

=#-3/2#

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Answer 2

Genesis Allen

To find the vertex of the function ( y = -x^2 - 3x - 6 ), you can use the formula for the x-coordinate of the vertex: ( x = \frac{-b}{2a} ). In this equation, ( a = -1 ) and ( b = -3 ). Substituting these values into the formula gives ( x = \frac{-(-3)}{2(-1)} = \frac{3}{-2} = -\frac{3}{2} ). To find the corresponding y-coordinate, substitute ( x = -\frac{3}{2} ) into the equation: ( y = -(-\frac{3}{2})^2 - 3(-\frac{3}{2}) - 6 = -\frac{9}{4} + \frac{9}{2} - 6 = -\frac{9}{4} + \frac{18}{4} - \frac{24}{4} = -\frac{15}{4} ). Therefore, the vertex of the function is ( \left(-\frac{3}{2}, -\frac{15}{4}\right) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.