Quadratic Transformation Rules

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

• a vertical translation shifting f(x) 4 units up

• a horizontal compression by a factor of 4

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

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

Which description of the transformation of the graph of f(x) = x² to the graph of g(x) = (3x)² + 2 is true?

• a horizontal compression by a factor of 1/3 with translation up two units

• a horizontal stretch by a factor of three with a translation right two units

• a vertical stretch by a factor of 3 with translation two units to the right

• a vertical compression by a factor of 1/3 with translation two units up

How did we transform from the parent function f(x) = x²?

• reflection over x-axis, vertical compression by a factor of 1/2, horizontal shift right one, vertical shift up three

• vertical compression by a factor of 1/2, horizontal shift left one, vertical shift up three

• reflection over the x-axis, horizontal shift right one, vertical shift down three

• no changes were made to y = x²

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.

"a" causes the parabola to vertically ​ (a)   when a > 1.

• stretch

• compress

a

b

c

d

e

left

reflected

down

right

up

"a" causes the parabola to vertically ​ (a)   when a < 1.

• compress

• stretch

Label how each number transforms the function

b

c

d

e

Right 3

Stretched by a factor of 2

Left 3

Moves up 7

Reflected over the x-axis

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

• A

• B

• C

• D

f

g

e

d