Quadratic Transformation

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a reflection across the line x = -4
• a reflection across the line y = -4
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

Which list orders the quadratic functions from narrowest to widest?

• y = x² 
  y = 4x² 
  y = 2x² - 2  
  y = 0.5 x²
• y = 0.5 x²  
   y = x² 
  y = 2x² - 2 
  y = 4x²
• y = 4x² 
  y = 2x² - 2
   y = x² 
  y = 0.5 x²  
•  y = 2x² - 2
   y = 4x²
   y = 0.5x²
   y = x²

Describe the change shown in the graph and equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= (x−3)²

• Vertex moves 5 up

• Vertex moves 3 down

• Vertex moves 3 to the right

• Stretched by a factor of 3

Describe the change shown in the graph and equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= 2x²

• Vertex moves 2 up

• Vertex moves 2 to the right

• Reflected over the x-axis

• Stretched(skinnier) by a factor of 2

Describe the change shown in the equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= x² + 4

• Moved 4 up

• Moved 4 to the right

• Stretched(skinnier) by a factor of 4

• Moved 4 to the left and 4 up

Describe the change shown in the equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= (x−4)²

• Moved 4 to the right

• Moved 4 to the left

• Moved 4 down

• Compressed (shrunk) by a factor of 4

Write the equation for g(x), the parabola in blue.

f(x)= x²

• g(x)= x² + 3

• g(x)= (x + 3)²

• g(x)= (x − 3)²

• g(x)= 3x²

Which of the following transformations occurs when transforming the graph of y=x² to y=(x+1)² - 3? 

• Shift right 1 and down 3
• shift left 1 and down 3
• shift right 1 and up 3 
• shifts left 3 and up 1

If the graph of the quadratic parent function f(x)=x² is translated 3 units to the right and 2 units down, which of the following equations describes the translated graph? 

• y = (x + 2)² + 3
• y = (x - 3)² + 2
• y = (x + 3)² - 2
• y = (x - 3)² - 2

If a = 5, how does the graph of g(x) differ from the graph of f(x)?

• The vertex is 5 units higher

• The vertex is 5 units lower

• It is narrower

• It is wider