Quadratic Graphing and Imaginary Numbers
1. Graph the function and fill out the rest of the
information.
2
● Function: 𝑦 = 𝑥 + 4𝑥 + 2
○ 𝑎 = 1, 𝑏 = 4, 𝑐 = 2
● Axis of Symmetry:
−𝑏 −4
● 𝑥 = 2𝑎
→𝑥 = 2(1)
→ 𝑥 =− 2
● Vertex Calculation:
2
○ 𝑦 = (− 2) + 4(− 2) + 2 = 4 − 8 + 2 =− 2 → 𝑉𝑒𝑟𝑡𝑒𝑥: (− 2, − 2)
○ Additional points:
2
■ For 𝑥 =− 3: 𝑦 = (− 3) + 4(− 3) + 2 = 9 − 12 + 2 =− 1
2
■ For 𝑥 =− 4: 𝑦 = (− 4) + 4(− 4) + 2 = 16 − 16 + 2 = 2
● Summary of Properties:
○ Vertex: (− 2, − 2)
○ Axis of Symmetry: 𝑥 =− 2
○ Max or Min Value: Min value: − 2
○ Domain: (− ∞, ∞)
○ Range: [− 2, ∞)
, 2. Graph the function and fill out the rest of the
information.
2
● Function: 𝑦 = (𝑥 − 6) − 4
● Table of Values:
○ 𝑥 = 5, 𝑦 =− 4
○ 𝑥 = 6, 𝑦 =− 3
○ 𝑥 = 7, 𝑦 = 0
● Summary of Properties:
○ Vertex: (5, − 4)
○ Axis of Symmetry: 𝑥 = 6 (Note: based on standard vertex form
2
𝑦 = 𝑎(𝑥 − ℎ) + 𝑘, axis of symmetry is 𝑥 = 5)
○ Max or Min Value: − 4
○ Domain: (− ∞, ∞)
○ Range: [− 4, ∞)
1. Graph the function and fill out the rest of the
information.
2
● Function: 𝑦 = 𝑥 + 4𝑥 + 2
○ 𝑎 = 1, 𝑏 = 4, 𝑐 = 2
● Axis of Symmetry:
−𝑏 −4
● 𝑥 = 2𝑎
→𝑥 = 2(1)
→ 𝑥 =− 2
● Vertex Calculation:
2
○ 𝑦 = (− 2) + 4(− 2) + 2 = 4 − 8 + 2 =− 2 → 𝑉𝑒𝑟𝑡𝑒𝑥: (− 2, − 2)
○ Additional points:
2
■ For 𝑥 =− 3: 𝑦 = (− 3) + 4(− 3) + 2 = 9 − 12 + 2 =− 1
2
■ For 𝑥 =− 4: 𝑦 = (− 4) + 4(− 4) + 2 = 16 − 16 + 2 = 2
● Summary of Properties:
○ Vertex: (− 2, − 2)
○ Axis of Symmetry: 𝑥 =− 2
○ Max or Min Value: Min value: − 2
○ Domain: (− ∞, ∞)
○ Range: [− 2, ∞)
, 2. Graph the function and fill out the rest of the
information.
2
● Function: 𝑦 = (𝑥 − 6) − 4
● Table of Values:
○ 𝑥 = 5, 𝑦 =− 4
○ 𝑥 = 6, 𝑦 =− 3
○ 𝑥 = 7, 𝑦 = 0
● Summary of Properties:
○ Vertex: (5, − 4)
○ Axis of Symmetry: 𝑥 = 6 (Note: based on standard vertex form
2
𝑦 = 𝑎(𝑥 − ℎ) + 𝑘, axis of symmetry is 𝑥 = 5)
○ Max or Min Value: − 4
○ Domain: (− ∞, ∞)
○ Range: [− 4, ∞)
