Answer :
To determine the direction a parabola opens based on the given equation [tex]\( y = ax^2 \)[/tex] and the sign of [tex]\( a \)[/tex], let's analyze the properties of parabolas:
1. General Form of a Parabola: The standard form of a quadratic equation representing a parabola is [tex]\( y = ax^2 \)[/tex].
2. Role of Coefficient [tex]\( a \)[/tex]: The coefficient [tex]\( a \)[/tex] dictates the parabola's orientation:
- If [tex]\( a \)[/tex] is positive, the parabola opens upwards.
- If [tex]\( a \)[/tex] is negative, the parabola opens downwards.
3. Given Condition: In this problem, it is specified that [tex]\( a \)[/tex] is negative.
Since [tex]\( a \)[/tex] is negative, our parabola opens downwards.
Therefore, the correct answer is:
OC. Down
1. General Form of a Parabola: The standard form of a quadratic equation representing a parabola is [tex]\( y = ax^2 \)[/tex].
2. Role of Coefficient [tex]\( a \)[/tex]: The coefficient [tex]\( a \)[/tex] dictates the parabola's orientation:
- If [tex]\( a \)[/tex] is positive, the parabola opens upwards.
- If [tex]\( a \)[/tex] is negative, the parabola opens downwards.
3. Given Condition: In this problem, it is specified that [tex]\( a \)[/tex] is negative.
Since [tex]\( a \)[/tex] is negative, our parabola opens downwards.
Therefore, the correct answer is:
OC. Down
