Question

Complete the table below and graph on the same coordinate plane. Then analyze the relationship between the graphs.

4. Given: y = 2x2 – 4x + 4

Domain
Range
Opening of the parabola
Vertex
Axis of Symmetry
x - intercept
y – intercept
Domain
Range
Opening of the parabola
Vertex
Axis of Symmetry
x - intercept
y – intercept
Domain
Range
Opening of the parabola
Vertex
Axis of Symmetry
x - intercept
y – intercept

Answer 1

Answer:

Solution:

y = - 2x²

Domain    ∈ R

Range      (-∞ , 0]

opening of parabola - Vertical Downward

Vertex  = ( 0 , 0)

Axis of symmetry   y axis  ( x = 0)

x - intercept    (0 , 0)

y intercept      (0 , 0)

 

y =  -  x² + 4

Domain    ∈ R

Range      (-∞ , 4]

opening of parabola - Vertical Downward

Vertex  = ( 0 , 4)

Axis of symmetry   y axis  ( x = 0)

x - intercept    (-2 , 0) , ( 2 , 0)

y intercept      (0 , 4)

y =  (x+1)²

Domain    ∈ R

Range      [0 , ∞)

opening of parabola - Vertical upward

Vertex  = ( -1 , 0)

Axis of symmetry   x= -1   parallel to y axis

x - intercept    (-1 , 0)

y intercept      (0 , 1)

y = 2x² - 4x + 4 -= 2(x - 1)² + 2

Domain    ∈ R

Range      [2 , ∞)

opening of parabola - Vertical upward

Vertex  = ( -1 , 2)

Axis of symmetry   x=  1   parallel to y axis

x - intercept    None

y intercept      (0 , 4)

Step-by-step explanation: