
F(x)=4x-x^2 f(x)=x^2 +2x-3 y= 3x^2-x


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It seems like you've provided three different polynomial functions:
- F(x) = 4x - x^2
- f(x) = x^2 + 2x - 3
- y = 3x^2 - x
These are all quadratic functions, which are polynomials of degree 2. Let's discuss each of them separately:
F(x) = 4x - x^2: This is a quadratic function that can be graphed as a downward-facing parabola. It has a leading coefficient of -1, which means the parabola opens downwards. The vertex of this parabola can be found by completing the square, and it is at (2, 4), and the axis of symmetry is x = 2.
f(x) = x^2 + 2x - 3: This is also a quadratic function, and it can be graphed as an upward-facing parabola. It has a leading coefficient of 1, which means the parabola opens upwards. To find the vertex, you can complete the square, and it is at (-1, -4), with the axis of symmetry being x = -1.
y = 3x^2 - x: This is another quadratic function with a leading coefficient of 3, meaning the parabola opens upwards and is stretched vertically compared to the standard parabola y = x^2. To find the vertex, complete the square, and it is at (1/6, -1/12), with the axis of symmetry being x = 1/6.
If you have any specific questions about these functions or if you'd like to perform any particular operations or calculations with them, please let me know!


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