What is the vertex of # y=-3x^2-4x+2(x-2)^2 #?

Answer 1

(4,24)

Simplify first #y= -3x^2-4x+2(x-2)^2# #y= -3x^2 -4x + 2(x^2+4x+4)# #y= -3x^2 -4x + 2x^2 +8x+8# #y= -x^2 +8x+8#
Now to solve for the vertex algebraically , we use the formula Vertex= #( -b/(2a) , f(-b/(2a) ) )# #-b/(2a) = 4# #f(4)= 24#

Vertex is (4,24).

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Answer 2

To find the vertex of the quadratic function ( y = -3x^2 - 4x + 2(x - 2)^2 ), you need to convert it to the standard form ( y = ax^2 + bx + c ), where the vertex is given by the point ( \left( -\frac{b}{2a}, f\left( -\frac{b}{2a} \right) \right) ).

First, expand and simplify the given function:

( y = -3x^2 - 4x + 2(x^2 - 4x + 4) ) ( y = -3x^2 - 4x + 2x^2 - 8x + 8 ) ( y = -x^2 - 12x + 8 )

Now, the coefficients are ( a = -1 ) and ( b = -12 ). Plug these into the formula for the x-coordinate of the vertex:

( x_{\text{vertex}} = -\frac{b}{2a} = -\frac{-12}{2(-1)} = -\frac{-12}{-2} = 6 )

To find the y-coordinate, plug ( x_{\text{vertex}} = 6 ) into the function:

( y = -(6)^2 - 12(6) + 8 = -36 - 72 + 8 = -100 )

So, the vertex of the function is ( (6, -100) ).

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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.

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.

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.

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.

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