Transformations of Quadratic Equations

Let the graph of g be a vertical stretch by a factor of 5 of the graph of f(x) = x². Write a rule for g.

• g(x) = 5x²

• g(x) = -5x²

• g(x) = x² + 5

• g(x) = (x + 5)²

Let the graph of g be a translation 7 units right and 12 units up of the graph of f(x) = (x + 3)² - 8. Write a rule for g.

• g(x) = (x - 4)² + 4

• g(x) = (x + 10)² + 4

• g(x) = (x - 4)² - 20

• g(x) = (x + 10)² - 20

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

Let the graph of g be a translation 7 units right and 12 units up of the graph of f(x) = x². Write a rule for g.

• g(x) = (x + 7)² + 12

• g(x) = (x + 12)² + 7

• g(x) = (x - 7)² - 12

• g(x) = (x - 7)² + 12

For g(x) = (x - 10)² - 4, describe the transformation from the parent function.

• Slide left 10 and down 4 units

• Slide right 10 and down 4 units

• Slide left 10 and up 4 units

• Slide right 10 and up 4 units

What steps transform the graph y = x² to y = (x - 4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Identify the vertex of f(x) = 5(x+6)² - 7

• (5,6)

• (0,0)

• (6,-7)

• (-6,-7)

Let the graph of g be a translation 7 units right and a reflection in the x-axis of the graph of f(x) = x². Write a rule for g.

• g(x) = -(x - 7)²

• g(x) = (x - 7)²

• g(x) = -(x + 7)²

• g(x) = (x + 7)²

Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f(x) = x² + 2. Write a rule for g.

• g(x) = 3x² + 6

• g(x) = -3x² - 6

• g(x) = -3x² - 2

• g(x) = 3x² + 2

Match the equation to its description.

• Stretched by 4 and up 4

• Compressed by 4 and up 4

• Stretched by 4 and left 4

• Compressed by 4 and left 4