Answer :
To determine which way the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens when the coefficient [tex]\( a \)[/tex] is negative, let's analyze the general form of a quadratic equation and the properties of parabolas.
1. Understanding the Equation: The given equation is [tex]\( y = ax^2 \)[/tex], where [tex]\( y \)[/tex] is expressed in terms of [tex]\( x \)[/tex], and [tex]\( a \)[/tex] is a constant coefficient.
2. Coefficient [tex]\( a \)[/tex]: The value of [tex]\( a \)[/tex] determines the direction in which the parabola opens:
- If [tex]\( a > 0 \)[/tex], the parabola opens upwards.
- If [tex]\( a < 0 \)[/tex], the parabola opens downwards.
3. Given Condition: The problem states that the coefficient [tex]\( a \)[/tex] is negative.
4. Analysis of the Parabola's Direction:
- When [tex]\( a \)[/tex] is negative (i.e., [tex]\( a < 0 \)[/tex]), the parabola opens downwards. This is because the quadratic term [tex]\( ax^2 \)[/tex] will dominate the function, and since [tex]\( a \)[/tex] is negative, the value of [tex]\( y \)[/tex] will decrease as [tex]\( |x| \)[/tex] increases, creating a "downward" shape for the parabola.
5. Conclusion: Based on the analysis, when [tex]\( a \)[/tex] is negative, the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens downwards.
Therefore, the correct answer is:
○ C. Down
1. Understanding the Equation: The given equation is [tex]\( y = ax^2 \)[/tex], where [tex]\( y \)[/tex] is expressed in terms of [tex]\( x \)[/tex], and [tex]\( a \)[/tex] is a constant coefficient.
2. Coefficient [tex]\( a \)[/tex]: The value of [tex]\( a \)[/tex] determines the direction in which the parabola opens:
- If [tex]\( a > 0 \)[/tex], the parabola opens upwards.
- If [tex]\( a < 0 \)[/tex], the parabola opens downwards.
3. Given Condition: The problem states that the coefficient [tex]\( a \)[/tex] is negative.
4. Analysis of the Parabola's Direction:
- When [tex]\( a \)[/tex] is negative (i.e., [tex]\( a < 0 \)[/tex]), the parabola opens downwards. This is because the quadratic term [tex]\( ax^2 \)[/tex] will dominate the function, and since [tex]\( a \)[/tex] is negative, the value of [tex]\( y \)[/tex] will decrease as [tex]\( |x| \)[/tex] increases, creating a "downward" shape for the parabola.
5. Conclusion: Based on the analysis, when [tex]\( a \)[/tex] is negative, the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens downwards.
Therefore, the correct answer is:
○ C. Down
