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:
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) + 1
F(3/4) = 2(9/16) - 9/4 + 1
F(3/4) = 18/16 - 9/4 + 1
F(3/4) = 9/8 - 9/4 + 1
F(3/4) = 9/8 - 18/8 + 8/8
F(3/4) = -1/8
Therefore, the vertex of the parabola is at (3/4, -1/8).