Transformations of Quadratic Functions

Match the description to its equation.Moves right 7 (a)  

• A

• B

• C

• D

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)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• 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)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²

The quadratic parent function and the following function are graphed on a coordinate plane. Which statement is true?

• The graph of f is narrower than the parent function

• The graph of f is wider than the parent function.

• The graph of f is 7 units below the parent function.

• The graph of f is 7 units above the parent function.

1. Let the graph of g be a vertical stretch by a factor of 5 and a reflection in the x-axis, followed by a translation 9 units up of the graph of f(x) = x². Write a rule for g and identify the vertex.

• 1. g(x) = -5x² - 9

  3. Vertex (h, k) = (0, -9)

• g(x) = -5x² + 9

  Vertex (h, k) = (0, 9)

• g(x) = -9x² + 5

  Vertex (h, k) = (-9, 5)

• g(x) = 9x² - 5

  Vertex (h, k) = (9, -5)

Let the graph of g be a vertical stretch by a factor of 4 and a reflection in the x-axis, followed by a translation 7 units down of the graph of f(x) = x². Write a rule for g and identify the vertex.

• g(x) = -4x² - 7

  Vertex (h, k) = (0, -7)

• g(x) = -4x² + 7

  Vertex (h, k) = (0, 7)

• g(x) = -7x² + 4

  Vertex (h, k) = (-7, 4)

• g(x) = 7x² - 4

  Vertex (h, k) = (7, -4)

Let the graph of g be a translation 3 units right and 4 units up, followed by a reflection in the y-axis of the graph of f(x) = x² − 5x. Write a rule for g.

• g(x) = x² - 11x +28

• g(x) = x² + 11x - 28

• g(x) = x² + 11x +28

• g(x) = x² - 11x - 28

Let the graph of g be a translation 3 units right and 2 units down, followed by a reflection in the y-axis of the graph of f(x) = x² − 5x. Write a rule for g.

• g(x) = x² - 11x +22

• g(x) = x² + 11x - 22

• g(x) = x² + 11x +22

• g(x) = x² - 11x - 22

The height h (in feet) of water spraying from a fire hose can be modeled by h(x) = −0.03x² + x + 25, where x is the horizontal distance (in feet) from the fire truck. The crew raises the ladder so that the water hits the ground 10 feet farther from the fire truck. Write a function that models the new path of the water.

• g(x) = −0.03x² + x + 25

• g(x) = −0.03x² + x - 25

• g(x) = −0.03x² + x - 48

• g(x) = −0.03x² + x + 48

The height h (in feet) of water spraying from a fire hose can be modeled by h(x) = −0.03x² + x + 25, where x is the horizontal distance (in feet) from the fire truck. The crew raises the ladder so that the water hits the ground 20 feet farther from the fire truck. Write a function that models the new path of the water. 

• g(x) = −0.03x² + x + 77

• g(x) = −0.03x² + x - 77

• g(x) = −0.03x² - x - 77

• a g(x) = −0.03x² + x - 77