Perform the given transformations using the given function

Question

 y=2x^2+4

Vertical translation down 7,

horizontal translation to the left 3, vertical shrink by a factor of 2,

flip over the x-axis,

horizontal stretch by a factor of 3

Answer 1

y = 2x² + 4

• Vertical translation down 7:y = 2x² + 4 - 7 = 2x² - 3
• Horizontal translation to the left 3: y = 2(x+3)² - 3
• Vertical shrink by a factor of 2: y = (1/2)2(x+3)² - 3 = (x+3)² - 3
• Flip over the x-axis: y = -(x+3)² - 3
• Horizontal stretch by a factor of 3:  y = -(3(x+3))² - 3

Answer 2

y= 2(x² + 2)

 

y₁ = 2(x² + 2) - 7

 

y₂ = 2((x+3)² + 2) -7

 

y₃ =  ((x+3)² +2) - 7       (1/2)2 =1

 

y₄ = —(((x + 3)² + 2) - 7) or –((x + 3)² +2) + 7

 

y₅ = –((1/3)(x + 3)²) + 7

 

A²