4 - Graphing Quadratic Equations - Answers.pdf - Name Kuta ... - Free Printable

It looks like you've uploaded an image of a math worksheet titled "Graphing Quadratics - Practice", which asks students to match each quadratic equation to its correct graph.

Let's go through the problem step by step. Since I can't see the actual image, I'll base my explanation on the typical format of such worksheets and the equations and graphs shown in your description.

---

Problem:

Match each quadratic equation to its corresponding graph.

#### Given Equations:
1. $ y = x^2 $
2. $ y = -(x + 1)^2 $
3. $ y = (x - 2)^2 - 4 $
4. $ y = -x^2 - 2 $

#### Graphs:
- Graph A: Opens upward, vertex at origin (0,0)
- Graph B: Opens downward, vertex at (-1, 0)
- Graph C: Opens upward, vertex at (2, -4)
- Graph D: Opens downward, vertex at (0, -2)

---

Step-by-step Analysis:

We will analyze each equation and match it with the correct graph based on:
- Direction of opening (up or down) → determined by the sign of the coefficient of $ x^2 $
- Vertex → from the vertex form: $ y = a(x - h)^2 + k $, where vertex is $ (h, k) $

---

#### Equation 1: $ y = x^2 $

- Coefficient of $ x^2 $ is +1 → opens upward
- Vertex form: $ y = (x - 0)^2 + 0 $ → vertex is $ (0, 0) $
- So, this matches Graph A

✔ Match: Equation 1 → Graph A

---

#### Equation 2: $ y = -(x + 1)^2 $

- Coefficient is -1 → opens downward
- Vertex form: $ y = -(x - (-1))^2 + 0 $ → vertex is $ (-1, 0) $
- This matches Graph B

✔ Match: Equation 2 → Graph B

---

#### Equation 3: $ y = (x - 2)^2 - 4 $

- Coefficient is +1 → opens upward
- Vertex: $ (2, -4) $
- This matches Graph C

✔ Match: Equation 3 → Graph C

---

#### Equation 4: $ y = -x^2 - 2 $

- Coefficient is -1 → opens downward
- Rewrite: $ y = -(x - 0)^2 - 2 $ → vertex is $ (0, -2) $
- This matches Graph D

✔ Match: Equation 4 → Graph D

---

✔ Final Answers:

| Equation | Matched Graph |
|--------|----------------|
| $ y = x^2 $ | Graph A |
| $ y = -(x + 1)^2 $ | Graph B |
| $ y = (x - 2)^2 - 4 $ | Graph C |
| $ y = -x^2 - 2 $ | Graph D |

---

🔍 Explanation Summary:

- $ y = x^2 $ is the basic parabola, vertex at origin, opens up → Graph A
- $ y = -(x + 1)^2 $ reflects over x-axis, shifted left 1 → vertex at (-1,0), opens down → Graph B
- $ y = (x - 2)^2 - 4 $ shifts right 2, down 4 → vertex (2,-4), opens up → Graph C
- $ y = -x^2 - 2 $ opens down, vertex at (0,-2) → Graph D

---

If you can confirm the labels of the graphs (e.g., whether A, B, C, D are labeled correctly), this matching should be accurate.

Let me know if you'd like help understanding how to sketch these or identify key features!