Translating Quadratic Equations

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x)=3x²
• B.  g(x)=1/3x²
• C.  g(x) = x² - 3
• D.  g(x) = (x-3)²

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = 2x²
• B.  g(x) = 1/2x²
• C.  g(x) = x² + 2
• D.  g(x) = (x + 2)²

Let the graph of g be a translation 2 units down and 4 units left of the graph of f(x) = x². Write a rule for g.

• g(x) = (x - 4)² - 2

• g(x) = (x + 4)² - 2

• g(x) = (x - 4)² + 2

• g(x) = (x + 4)² + 2

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 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 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

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

• g(x) = x² + 7

• g(x) = -x² + 7

• g(x) = -x² - 7

• g(x) = -7x²

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

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

For g(x) = 2(x + 3)², describe the transformation from the parent function.

• Vertical stretch by factor of 2, slide left 3 units

• Vertical stretch by factor of 2, slide right 3 units

• Slide up 2 units and left 3 units

• Slide up 2 units and right 3 units