Characteristics and Transformations of Quadratic Functions

Identify the function graphed here.

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

What transformations occurred to get f(x), the red graph, to become 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 vertex of this parabola?

Hint: The highest or lowest point of the U

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

Vertex: ​ (a)  

Y-intercept: ​ (b)  

Axis of Symmetry: ​ (c)  

Max or min: ​ (d)  

Max or Min value:​ (e)  

• (3,4)

• (0,-5)

• x = 3

• Max

• y = 4

• 4,3

• (4,3)

• (-5,0)

• y = 3

• Min

Vertex: ​ (a)   Y-intercept: ​ (b)   Axis of Symmetry: ​ (c)   Max or min: ​ (d)   Range:​ (e)  

• (3,4)

• (0,-5)

• x = 3

• Max @ y = 4

• ( -∞, 4]

• (4,3)

• (-5,0)

• y = 3

• [4, ∞)

• Min @ y = -5

Vertex: ​ (a)  

Y-intercept: ​ (b)  

Axis of Symmetry: ​ (c)  

Max or min: ​ (d)  

Range:​ (e)  

• (3,4)

• (0,-5)

• x = 3

• Max @ y = 4

• ( -∞, 4]

• (4,3)

• (-5,0)

• y = 3

• [4, ∞)

• Min @ y = -5

Label the graph. Match the zero smaller and larger values by placing the box on the graph next to what it represents.

g

f

b

e

a

Vertex (-2, 4)

Axis of Symmetry: x = -4

Zero larger value

Axis of Symmetry: x = 0

Zero smaller value

Axis of Symmetry: x = -2

Minimum

Maximum

Vertex (-4, 2)

Label the graph. Match the zero smaller and larger values by placing the box on the graph next to what it represents.

f

h

c

b

e

Smaller Zero Value

Larger Zero Value

Maximum

Vertex (-4, 3)

Axis of Symmetry: x = 3

Minimum

Vertex (3, -4)

Axis of Symmetry: x = -4

• (0, 4)

• x = 2

• (4, 0)

• x = -2

• (2, 6)

• (5, 0)