To determine the direction in which the parabola opens for the quadratic equation [tex]\( y = 4x^2 - 8x - 4 \)[/tex], follow these steps:
1. Identify the coefficient of the [tex]\( x^2 \)[/tex] term: The general form of a quadratic equation is [tex]\( ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants.
- In the given equation [tex]\( y = 4x^2 - 8x - 4 \)[/tex], the coefficient [tex]\( a \)[/tex] of the [tex]\( x^2 \)[/tex] term is 4.
2. Determine the sign of the coefficient [tex]\( a \)[/tex]:
- Here, [tex]\( a = 4 \)[/tex], which is a positive number.
3. Analyze the sign of [tex]\( a \)[/tex]:
- If [tex]\( a \)[/tex] is positive, the parabola opens upwards.
- If [tex]\( a \)[/tex] is negative, the parabola opens downwards.
Since [tex]\( a = 4 \)[/tex] is positive, the parabola opens upwards.
Therefore, the correct answer is:
up
