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What is the vertex of #y= 2x^2 - 18x -6#?

Answer 1

#x_("vertex")=+9/2#
I will let you work out #y_("vertex")# by substitution

Write as:#" "y=2(x^2-18/2 x) -6#

Apply #" "(-1/2)xx(-18/2) = + 9/2#

#x_("vertex")=+9/2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
To derive #y_("vertex")# substitute #x=9/2# into the original equation and solve for y

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Answer 2

Julia Adams

The vertex of the quadratic function ( y = 2x^2 - 18x - 6 ) can be found using the formula ( x = \frac{-b}{2a} ), where ( a = 2 ) and ( b = -18 ). Substituting these values into the formula, we get ( x = \frac{-(-18)}{2 \times 2} = \frac{18}{4} = 4.5 ). To find the corresponding y-coordinate, substitute ( x = 4.5 ) into the original equation: ( y = 2(4.5)^2 - 18(4.5) - 6 ). Solving this equation yields ( y = -30 ). Therefore, the vertex of the function is ( (4.5, -30) ).

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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.