To determine whether the graph of y=3x^2-4x+2 opens downwards, we need to analyze the coefficient of x^2.
In the general form of a quadratic equation, y=ax^2+bx+c, the coefficient a determines whether the parabola opens upwards or downwards.
If a is positive, the parabola opens upwards. If a is negative, the parabola opens downwards.
In this case, the coefficient in front of x^2 is 3, which is positive. Therefore, the graph of y=3x^2-4x+2 does not open downwards. The statement is False.
To check if the graph of y=2x^2-4x+2 has a y-intercept of (0,1), we can substitute x=0 into the equation and see if we obtain y=1.
When x=0, we have:
y = 2(0)^2 - 4(0) + 2
y = 0 - 0 + 2
y = 2
The y-coordinate is 2, not 1. Therefore, the y-intercept of the graph is not (0,1). The statement is False.
In summary:
1. The graph of y=3x^2-4x+2 does not open downwards (False).
2. The graph of y=2x^2-4x+2 does not have a y-intercept of (0,1) (False).