Question

Identify the vertex, axis of symmetry, maximum, or minimum, domain and range of each function.

Answer 1

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

a) y = 2(x - 2)² + 5

        ↓       ↓      ↓

      a= +   h= 2   k= 5

Vertex: (h, k) = (2, 5)

Axis of Symmetry: x = h  →  x = 2  

Max/Min: "a" is positive → minimum

Domain: x = All Real Numbers

Range:  y ≥ k → y ≥ 5

b) y = -(x - 1)² + 2

        ↓       ↓      ↓

      a= -   h= 1   k= 2

Vertex: (h, k) = (1, 2)

Axis of Symmetry: x = h  →  x = 1  

Max/Min: "a" is negative → maximum

Domain: x = All Real Numbers

Range:  y ≤ k → y ≤ 2

c) y = -(x + 4)² + 0

        ↓       ↓      ↓

      a= -  h= -4   k= 0

Vertex: (h, k) = (-4, 0)

Axis of Symmetry: x = h  →  x = -4  

Max/Min: "a" is negative → maximum

Domain: x = All Real Numbers

Range:  y ≤ k → y ≤ 0

d) y = 1/3(x + 2)² - 1

        ↓       ↓      ↓

      a= +  h= -2   k= -1

Vertex: (h, k) = (-2, -1)

Axis of Symmetry: x = h  →  x = -2  

Max/Min: "a" is positive → minimum

Domain: x = All Real Numbers

Range:  y ≥ k → y ≥ -2