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Characteristics
Focus and Directrix
Min/Max
Transformations
Modeling
100

What is the vertex of the parabola?

f(x) = -2(x - 24)2 + 12

What is (24, 12)

100

Identify the focus (point) and directrix (line) of the parabola. 

y = (-1/16) x2

Focus: (0, -4)


Directrix: y = 4

100

Does the parabola have a minimum or a maximum?

f(x) = -3(x + 5)2

Maximum

100

Write an equation that is a vertical stretch by 2 of the parent function f(x) = x2

f(x) =2x2

100

Write and equation for the parabola that passes through (0, 9) and has a vertex of (0, 0)

y = 9x2

OR

y = 9(x + 0)2 +0

200

What are the x-intercepts?

f(x) = -2(x +6)(x -3)

(-6, 0) and (3, 0)

200

Identify the focus (point) and directrix (line) of the parabola. 

y = (1/28) x2

Focus: (0, 7)


Directrix: y = -7

200

Does this parabola have a min/max?


f(x) = -8(x - 2)2

Max

200

Write an equation that is 

      a vertical stretch by 2

      translated left 6 units

 of the parent function f(x) = x2

f(x) = 2(x + 6)2

200

Write an equation that passes though the point (2,1) and has a vertex of (-3, 4)

y= -0.12(x +3)2 + 4

300

What is the vertex of the parabola? What is the axis of Symmetry?

f(x) = -2(x +6)2 -2

vertex (-6, -2)


A.O.S: x = -6

300

Identify the focus (point) and directrix (line) of the parabola. 

4x =  y2

Focus: (1, 0)


Directrix: x = -1

300

Does the parabola have a min/max? What is the min/max value?


f(x) = 3(x - 2)2 + 4

min: 4

300

Write an equation that is 

      a x-axis reflection

      vertical stretch by 4

 of the parent function f(x) = x2

f(x) = -4x2

300

Write an equation that has the x-intercepts of (-3, 0) and (6, 0) and passes through the point (14, 544)

y = 4(x - 6)(x + 3)

400

What is the vertex of the parabola? What is the axis of Symmetry?

f(x) = -2x2 + 8x - 12

Vertex: (2, -4)


A.O.S: x = 2

400

Identify the focus (point) and directrix (line) of the parabola. 

-44x = y2

Focus: (-11, 0)


Directrix: x = 11

400

f(x) = -2(x + 4)2 - 3


Does the parabola have a min or a max? What is the min/max value?

What is the range(y-values)?

max: -3 

range: y less than or equal to -3

400

Write an equation that is 

      translated up 5 units

      translated right 2 units

      x-axis reflection

 of the parent function f(x) = x2

f(x) = -(x - 2)2 + 5

400

Write an equation that has the x-intercepts of (5, 0) and (25, 0) and passes though the point (-3 , -112)

y = -1/2(x - 5)(x - 25)

500

What is the vertex of the parabola? What is the axis of Symmetry?

f(x) = 4x2 -2x + 3

Vertex: (-1/4, 3 1/4)


A.O.S: x = -1/4

500

Identify the focus (point) and directrix (line) of the parabola. 

2y = x2

Focus: (1/2, 0)


Directrix: x = -1/2

500

f(x) = 8(x - 8)2 + 9


Does the parabola have a min or a max? What is the min/max value?

What is the range(y-values)?

min: 9

range: y greater than or equal to 9

500

Write an equation that is 

      translated down 1 unit

      translated right 7 units

      x-axis reflection and a vertical stretch by 3

 of the parent function f(x) = x2

f(x) =-3(x - 7)2 - 1