graphing quadratics wkst
date__________ period____
identify the vertex and write the axis of symmetry equation for each quadratic function.
1) $y = \frac{1}{2}(x + 4)^2 - 2$
2) $y = 3(x - 2)^2 + 3$
3) $y = (x + 3)^2 - 1$
4) $y = 2(x - 2)^2 - 2$
sketch the graph of each function.
5) $y = (x + 2)^2 - 2$
6) $y = (x + 2)^2 + 4$
7) $y = (x - 3)^2 - 2$
8) $y = (x + 3)^2 - 1$

Question

Accepted Answer

To solve these problems, we use the vertex form of a quadratic function $ y = a(x - h)^2 + k $, where the vertex is $ (h, k) $ and the axis of symmetry is $ x = h $. Let's correct the errors and solve each problem properly:

### Problem 1: $ y = \frac{1}{2}(x + 4)^2 - 2 $
- **Step 1: Identify $ h $ and $ k $**
  Rewrite $ (x + 4) $ as $ (x - (-4)) $. Thus, $ h = -4 $ and $ k = -2 $.
- **Step 2: Find the vertex**
  Vertex: $ (h, k) = (-4, -2) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = h = -4 $.

### Problem 2: $ y = 3(x - 2)^2 + 3 $
- **Step 1: Identify $ h $ and $ k $**
  Here, $ h = 2 $ and $ k = 3 $.
- **Step 2: Find the vertex**
  Vertex: $ (2, 3) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = 2 $.

### Problem 3: $ y = (x + 3)^2 - 1 $
- **Step 1: Identify $ h $ and $ k $**
  Rewrite $ (x + 3) $ as $ (x - (-3)) $. Thus, $ h = -3 $ and $ k = -1 $.
- **Step 2: Find the vertex**
  Vertex: $ (-3, -1) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = -3 $.

### Problem 4: $ y = 2(x - 2)^2 - 2 $
- **Step 1: Identify $ h $ and $ k $**
  Here, $ h = 2 $ and $ k = -2 $.
- **Step 2: Find the vertex**
  Vertex: $ (2, -2) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = 2 $.

### Problem 5: $ y = (x + 2)^2 - 2 $
- **Step 1: Identify $ h $ and $ k $**
  Rewrite $ (x + 2) $ as $ (x - (-2)) $. Thus, $ h = -2 $ and $ k = -2 $.
- **Step 2: Find the vertex**
  Vertex: $ (-2, -2) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = -2 $.

### Problem 6: $ y = (x + 2)^2 + 4 $
- **Step 1: Identify $ h $ and $ k $**
  Rewrite $ (x + 2) $ as $ (x - (-2)) $. Thus, $ h = -2 $ and $ k = 4 $.
- **Step 2: Find the vertex**
  Vertex: $ (-2, 4) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = -2 $.

### Problem 7: $ y = (x - 3)^2 - 2 $
- **Step 1: Identify $ h $ and $ k $**
  Here, $ h = 3 $ and $ k = -2 $.
- **Step 2: Find the vertex**
  Vertex: $ (3, -2) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = 3 $.

### Problem 8: $ y = (x + 3)^2 - 1 $
- **Step 1: Identify $ h $ and $ k $**
  Rewrite $ (x + 3) $ as $ (x - (-3)) $. Thus, $ h = -3 $ and $ k = -1 $.
- **Step 2: Find the vertex**
  Vertex: $ (-3, -1) $.
- **Step 3: Find the axis of symmetry**
  Axis of symmetry: $ x = -3 $.

### Final Answers (Vertex, Axis of Symmetry):
1. Vertex: $ \boldsymbol{(-4, -2)} $, Axis of Symmetry: $ \boldsymbol{x = -4} $
2. Vertex: $ \boldsymbol{(2, 3)} $, Axis of Symmetry: $ \boldsymbol{x = 2} $
3. Vertex: $ \boldsymbol{(-3, -1)} $, Axis of Symmetry: $ \boldsymbol{x = -3} $
4. Vertex: $ \boldsymbol{(2, -2)} $, Axis of Symmetry: $ \boldsymbol{x = 2} $
5. Vertex: $ \boldsymbol{(-2, -2)} $, Axis of Symmetry: $ \boldsymbol{x = -2} $
6. Vertex: $ \boldsymbol{(-2, 4)} $, Axis of Symmetry: $ \boldsymbol{x = -2} $
7. Vertex: $ \boldsymbol{(3, -2)} $, Axis of Symmetry: $ \boldsymbol{x = 3} $
8. Vertex: $ \boldsymbol{(-3, -1)} $, Axis of Symmetry: $ \boldsymbol{x = -3} $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( y = \frac{1}{2}(x + 4)^2 - 2 \)

Problem 2: \( y = 3(x - 2)^2 + 3 \)

Problem 3: \( y = (x + 3)^2 - 1 \)

Problem 4: \( y = 2(x - 2)^2 - 2 \)

Problem 5: \( y = (x + 2)^2 - 2 \)

Problem 6: \( y = (x + 2)^2 + 4 \)

Problem 7: \( y = (x - 3)^2 - 2 \)

Problem 8: \( y = (x + 3)^2 - 1 \)

Final Answers (Vertex, Axis of Symmetry):

Answer: