What is the vertex of # y=-3x^2-4x+2(x-2)^2 #?
(4,24)
Vertex is (4,24).
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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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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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