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The image contains a review of Unit 3: Quadratic Functions for Algebra 2. Here's a breakdown of the problem and instructions:

You are asked to identify key attributes of a given parabola.

### Given Equation:
The function to analyze is \( a(x) = -2x^2 + 5 \).

### Key Attributes to Identify:
1. **Vertex**: The highest or lowest point on the parabola.
2. **Axis of Symmetry (A.O.S)**: The vertical line that divides the parabola into two mirror images.
3. **Concavity**: Whether the parabola opens upwards or downwards.
4. **Max/Min**: The maximum or minimum value of the parabola.
5. **Domain**: All possible x-values for which the function is defined.
6. **Range**: All possible y-values that the function can take.

### Let's calculate these attributes:

#### 1. Vertex:
For the equation \( a(x) = -2x^2 + 5 \), the standard form is \( a(x) = ax^2 + bx + c \), where \( a = -2 \), \( b = 0 \), and \( c = 5 \). The x-coordinate of the vertex is found using:

\[
x = -\frac{b}{2a} = -\frac{0}{2(-2)} = 0
\]

Substitute \( x = 0 \) into the equation to find the y-coordinate of the vertex:

\[
y = -2(0)^2 + 5 = 5
\]

So, the vertex is \( (0, 5) \).

#### 2. Axis of Symmetry (A.O.S):
The axis of symmetry is given by the x-coordinate of the vertex, which is \( x = 0 \).

#### 3. Concavity:
Since the coefficient of \( x^2 \) is negative (\( -2 \)), the parabola opens **downward**.

#### 4. Max/Min:
Since the parabola opens downward, the vertex represents the **maximum** value. The maximum value is \( 5 \), occurring at \( x = 0 \).

#### 5. Domain:
The domain of a quadratic function is always all real numbers, so the domain is:

\[
(-\infty, \infty)
\]

#### 6. Range:
Since the parabola has a maximum value of 5 and opens downward, the range is:

\[
(-\infty, 5]
\]

---

Would you like more details on any of these points or have any questions?

### Follow-up Questions:
1. How do you calculate the axis of symmetry for a quadratic function in standard form?
2. What does the concavity of a parabola tell you about its behavior?
3. Can you explain how the range of a quadratic function depends on its maximum or minimum?
4. How would the attributes change if the coefficient of \( x^2 \) were positive?
5. What is the effect of the constant term on the graph of a quadratic function?

### Tip:
To find the vertex quickly, use the formula \( x = -\frac{b}{2a} \), which applies to all quadratic functions in standard form.

Identify key attributes of the parabola given by the quadratic function a(x) = -2x^2 + 5.

Learn how to identify key attributes of the quadratic function a(x) = -2x^2 + 5, including vertex, axis of symmetry, concavity, and the function's domain and range. This problem covers essential algebraic concepts like vertex calculation, axis of symmetry, and more. Suitable for students in Grades 9-11.

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