Transformations

Quadratic functions f and g are graphed. Graph g was horizontally compressed from the parent function. Which pair of functions could have been used to create the graphs of f and g?

• g(x) = (0.5x)² and f(x) = x²

• g(x) = (5x)² and f(x) = x²

• g(x) = 5x² and f(x) = x²

• g(x) = (x + 5)² and f(x) = x²

The graph of g(x) = x² is transformed to create the graph of h(x) = -g(x). Describe the transformation.

• Vertical shift up.

• Horizontal shift to the right.

• Reflection over the x-axis.

• Horizontal shift to the left.

The graph of g(x) = x² is transformed to create the graph of h(x) = 0.5g(x). Describe the transformation.

• Vertical stretch by a factor of 0.5.

• Vertical compression by a factor of 0.5

• Horizontal stretch by a factor of 0.5.

• Horizontal compression by a factor of 0.5.

Which transformations can be used to obtain the graph of h(x)= -x² - 3 from the function f(x) = x²?

• A reflection across the x-axis followed by a translation up 3 units.

• A reflection across the x-axis followed by a translation down 3 units.

• A reflection across the y-axis followed by a translation to the right 3 units.

• A reflection across the y-axis followed by a translation to the left 3 units.

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.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

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

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

If the blue graph is

f(x) = x²

then the red must be...

• g(x) = f(x) - 5

• g(x) = f(x) + 5

• g(x) = f(x - 5)

• g(x) = f(x + 5)

What transformations occurred to f(x), the red graph, to make g(x), the blue graph?

• horizontal shift down and vertical shift left

• horizontal shift left and vertical shift down

• horizontal shift right and vertical shift up

• horizontal shift up and vertical shift right

What is the name of the imaginary line that cuts a parabola in half and goes through the vertex?

• the middle
• axis of symmetry
• minimum
• standard form

Tags

CCSS.HSF-IF.C.7A

Find the solutions to

2x² + 7x - 15 = 0

• -1.5 & 5

• No Solution

• -5 & 1.5

• 0.7 & 5

Tags

CCSS.HSA-REI.B.4B