Answer: see below
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k where
- "a" is the vertical stretch (positive = min [U], negative = max [∩])
- (h, k) is the vertex
- Axis of Symmetry is always: x = h
- Domain is always: x = All Real Numbers
- Range is y ≥ k when "a" is positive or y ≤ k when "a" is negative
6) y = 3(x - 1)² + 0
↓ ↓ ↓
a= + h= 1 k= 0
Vertex: (h, k) = (1, 0)
Axis of Symmetry: x = h → x = 1
Max/Min: "a" is positive → minimum
Domain: x = All Real Numbers
Range: y ≥ k → y ≥ 0
7) y = -1/2(x + 6)² - 7
↓ ↓ ↓
a= - h= -6 k= -7
Vertex: (h, k) = (-6, -7)
Axis of Symmetry: x = h → x = -6
Max/Min: "a" is negative → maximum
Domain: x = All Real Numbers
Range: y ≤ k → y ≤ -7
8) y = -(x - 0)² - 3
↓ ↓ ↓
a= - h= 0 k= -3
Vertex: (h, k) = (0, -3)
Axis of Symmetry: x = h → x = 0
Max/Min: "a" is negative → maximum
Domain: x = All Real Numbers
Range: y ≤ k → y ≤ -3
