Alright, let's determine which direction the parabola opens given the equation [tex]\( y = ax^2 \)[/tex].
1. Understanding the Basic Equation:
The given equation [tex]\( y = ax^2 \)[/tex] is a standard form of a parabola. This is a quadratic equation where 'y' is expressed in terms of 'x'.
2. Coefficient 'a' and Its Significance:
- If the coefficient 'a' is positive ([tex]\( a > 0 \)[/tex]), it determines the direction in which the parabola opens.
- In general, for the equation [tex]\( y = ax^2 \)[/tex]:
- When [tex]\( a > 0 \)[/tex] (positive), the parabola opens upwards.
- When [tex]\( a < 0 \)[/tex] (negative), the parabola opens downwards.
3. Answering the Question:
Given that [tex]\( a \)[/tex] is positive, according to the above rules, the parabola will open upwards.
So, the correct option is:
[tex]\[ \text{B. Up} \][/tex]
Therefore, the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens upwards if [tex]\( a \)[/tex] is positive.
