To determine whether the graph of the quadratic equation [tex]\( y = 3x^2 - 4x + 2 \)[/tex] opens upward or downward, we need to consider the coefficient of the [tex]\( x^2 \)[/tex] term, which is denoted by [tex]\( a \)[/tex] in the general form of a quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex].
The behavior of the graph depends on the sign of [tex]\( a \)[/tex]:
- If [tex]\( a \)[/tex] is positive, the parabola (graph) opens upwards.
- If [tex]\( a \)[/tex] is negative, the parabola opens downwards.
In the given equation [tex]\( y = 3x^2 - 4x + 2 \)[/tex]:
- The coefficient [tex]\( a \)[/tex] is 3.
Since [tex]\( a = 3 \)[/tex] is positive, the graph of the equation opens upwards, not downwards.
Therefore, the statement "The graph of [tex]\( y = 3x^2 - 4x + 2 \)[/tex] opens downward" is:
B. False
