When the parabola opens, upward, then which.of the followfng condition must be satisfied?

Options

A. `Dgt0`
B. `alt0`
C. `agt0`
D. `agtbgtc`

Answer

To determine the condition that must be satisfied for a parabola to open upward, we follow these steps:

### Step 1: Understand the standard form of a quadratic equation
A quadratic equation can be expressed in the standard form as:
\[ y = ax^2 + bx + c \]
where \( a \), \( b \), and \( c \) are constants.

### Step 2: Identify the role of the coefficient \( a \)
The coefficient \( a \) in the quadratic equation plays a crucial role in determining the direction in which the parabola opens:
- If \( a > 0 \), the parabola opens **upward**.
- If \( a < 0 \), the parabola opens **downward**.

### Step 3: Analyze the options given in the question
The question provides several conditions:
1. \( D > 0 \)
2. \( A < 0 \)
3. \( A > 0 \)
4. \( A > B \)
5. \( B > C \)

### Step 4: Evaluate the conditions
- **Condition 1**: \( D > 0 \) - This condition relates to the discriminant of the quadratic equation and does not determine the direction of the parabola.
- **Condition 2**: \( A < 0 \) - This condition indicates that the parabola opens downward, which is not what we want.
- **Condition 3**: \( A > 0 \) - This condition indicates that the parabola opens upward, which is what we are looking for.
- **Condition 4**: \( A > B \) - This condition does not directly relate to the direction of the parabola.
- **Condition 5**: \( B > C \) - This condition also does not directly relate to the direction of the parabola.

### Step 5: Conclusion
The only condition that must be satisfied for the parabola to open upward is:
\[ A > 0 \]

### Final Answer
The condition that must be satisfied for the parabola to open upward is:
**A is greater than 0.**

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