quadratic transformations

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

Tags

TEKS.MATH.A.7C

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

• Maria throws the ball 10 times harder than Pablo does.
• Maria starts her ball at a height 10 feet higher than Pablo does.
• Pablo throws the ball 10 times harder than Maria does.
• Pablo starts his ball at a height 10 feet higher than Maria does.

Tags

CCSS.HSA.SSE.A.1

Match the description to its equation.
- moves down 3

• A
• B
• C
• D

Tags

CCSS.HSF.BF.B.3

Match the description to its equation.
Moves right 7

• A
• B
• C
• D

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

If the blue is f(x)=x^2, then the red must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

How do the graphs of the functions
f(x) = x² + 9 and
g(x) = x² – 11 relate to each other?

• The graph of f(x) is 2 units above the graph of g(x).
• The graph of f(x) is 20 units above the graph of g(x).
• The graph of f(x) is 2 units to the right the graph of g(x).
• The graph of f(x) is 20 units to the right the graph of g(x).

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Describe the transformation of function f to g if

f(x)=x² and g(x)=(x - 4)²

• Vertical translation up

• Vertical translation down

• Horizontal translation left

• Horizontal translation right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Which transformation will occur if f(x) = x² is replaced with -f(x)?

• Nothing happens, it stays the same.
• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

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)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7