F(x)=2x^2-3x+1

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вопрос

The function given is a quadratic function in the form of F(x) = 2x^2 - 3x + 1. This function represents a parabola that opens upwards. The coefficient of x^2 is 2, which means the parabola is narrower than the standard parabola with a coefficient of 1.

The vertex of the parabola can be found using the formula x = -b/(2a), where a = 2 and b = -3. Substituting these values into the formula, we get:

x = -(-3)/(2*2) = 3/4

To find the y-coordinate of the vertex, we substitute x = 3/4 back into the original function:

F(3/4) = 2(3/4)^2 - 3(3/4) +
F(3/4) = 2(9/16) - 9/4 +
F(3/4) = 18/16 - 9/4 +
F(3/4) = 9/8 - 9/4 +
F(3/4) = 9/8 - 18/8 + 8/
F(3/4) = -1/8

Therefore, the vertex of the parabola is at (3/4, -1/8).