To determine the direction that the parabola described by the quadratic equation [tex]\( y = -4x^2 - 8x - 7 \)[/tex] opens, we need to analyze the coefficient of the [tex]\( x^2 \)[/tex] term.
1. Identify the quadratic equation form:
A quadratic equation generally is in the form [tex]\( y = ax^2 + bx + c \)[/tex], where:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex]
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex]
- [tex]\( c \)[/tex] is the constant term
2. Extract the coefficient [tex]\( a \)[/tex]:
In the given equation, [tex]\( y = -4x^2 - 8x - 7 \)[/tex]:
- The coefficient [tex]\( a \)[/tex] is [tex]\( -4 \)[/tex].
3. Determine the direction of the parabola:
- If [tex]\( a > 0 \)[/tex], the parabola opens upwards.
- If [tex]\( a < 0 \)[/tex], the parabola opens downwards.
Since [tex]\( a = -4 \)[/tex], which is less than 0, the parabola opens downwards.
Therefore, the direction that this parabola opens is:
down
