Shifting the Vertex of Quadratics

Which function's graph is the result of shifting the graph of f(x)=-x²-4 3 units down?

• g(x)=-x²-1

• g(x)=-4x²-4

• g(x) = -1/3x²-4

• g(x)=-x²-7

Describe the transformations from f(x)=x² to g(x)=1/4x²+4

• Reflected across x axis, up 4 units

• Vertical shrink by 1/4, up 4 units

• Vertical stretch by 4, up 4 units

• Vertical string by 1/4, left 4 units

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)

• (-6, 5)

• (-4, 3)

• (-4, 7)

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

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

Match each quadratic equation to its vertex

• (3, 5)

• j(x) = (x - 5)² + 3

• (-3, 5)

• y = (x + 5)² - 3

• (-5, -3)

• g(x) = (x + 3)² + 5

• (5, 3)

• h(x) = (x - 3)² - 5

• (3, -5)

• f(x) = (x - 3)² + 5

What is the vertex of y=(x + 2)² - 1?

• (2,1)

• (-2,1)

• (0,0)

• (-2,-1)

In the graph of the function y=x², which describes a vertical shift in the parent function up 5 units?

• y = x² - 5

• y = x² + 5

• y = (x - 5)²

• y = (x + 5)²

The graph of m(x) = x² was transformed to create the graph of n(x) = x² + 21.  Which of these describes the transformation?

• A vertical shift down 21 units.

• A vertical shift up 21 units.

• A horizontal shift to the right 21 units.

• A horizontal shift to the left 21 units.