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Let's analyze and solve the questions one by one.

Given the function:
\[
f(x) = 2x^2 + 4x - 5
\]

### 1. Does the parabola open up or down?
Since the coefficient of \( x^2 \) (which is 2) is positive, the parabola opens **up**. Therefore, it is **concave up**.

### 2. Is the vertex a maximum or a minimum?
Since the parabola opens upwards, the vertex will be at the lowest point, which means it is a **minimum**.

### 3. What is the y-intercept? 
To find the y-intercept, substitute \( x = 0 \) into the function:
\[
f(0) = 2(0)^2 + 4(0) - 5 = -5
\]
So, the y-intercept is the point **(0, -5)**.

### 4. What is the x-coordinate of the vertex?
The x-coordinate of the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
where \( a = 2 \) and \( b = 4 \). Substituting the values:
\[
x = -\frac{4}{2(2)} = -\frac{4}{4} = -1
\]

### 5. What is the y-coordinate of the vertex?
To find the y-coordinate, substitute \( x = -1 \) into the function:
\[
f(-1) = 2(-1)^2 + 4(-1) - 5 = 2(1) - 4 - 5 = 2 - 4 - 5 = -7
\]
So, the vertex is at **(-1, -7)**.

### Summary of Answers:
1. **Concave up**
2. **Minimum**
3. **(0, -5)**
4. **x = -1**
5. **y = -7**

Would you like further details or explanations on any of these steps? Here are some related questions to deepen your understanding:

1. How do you determine if a parabola opens up or down based on its equation?
2. Why does the sign of the coefficient \( a \) determine if the vertex is a maximum or minimum?
3. How do you find the vertex form of a quadratic equation from its standard form?
4. Can you explain how the vertex formula, \( x = -\frac{b}{2a} \), is derived?
5. What does the vertex tell you about the graph of a quadratic function?

**Tip:** Remember, the vertex formula \( x = -\frac{b}{2a} \) always helps locate the axis of symmetry of a parabola.

Given the function f(x) = 2x^2 + 4x - 5, determine the following information: 1. Does the parabola open up or down? 2. Is the vertex a maximum or a minimum? 3. What is the y-intercept as an (x, y) ordered pair? 4. What is the x-coordinate of the vertex? 5. What is the y-coordinate of the vertex?

Learn how to analyze the quadratic function f(x) = 2x^2 + 4x - 5. This problem covers determining the concavity, vertex, y-intercept, and finding both coordinates of the vertex using algebraic methods. Suitable for students in Grades 9-10.

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