Transformations of Parabolas
Features of
Parabolas
Parabolas
Standard
Form
Form
Vertex
Form
Form
Factored
Form
Form
100
Given the following equation, name the vertical shift of the parabola from the parent graph.
y = -2(x - 3)2 - 7
Vertical shift down 7
100
Given the graph below, find the x-intercept(s), y-intercept, the equation of the axis of symmetry, the vertex, dilation, and determine if the vertex is a maximum or a minimum then find the value.
Vertex: (-2, 8)
Axis of symmetry: x = -2
Max = 8
Dilation: 2
y-intercept: (0, 0)
x-intercept(s): (0, 0) and (-4, 0)
100
Convert the following equation to standard form.
y = (k + 1)(k - 5)
y = k2 - 4k - 5
100
Convert the following equation to vertex form.
y = x2 + 10x + 23
y = (x + 5)2 - 2
100
Convert the following equation to factored form.
y =v2 + 8v + 12
y = (v + 6)(v + 2)
200
Given the following equation, name the horizontal shift of the parabola from the parent graph.
y = 4(x + 2)2 + 9
Horizontal Shift left 2
200
Given the table below, find the x-intercept(s), y-intercept, the equation of the axis of symmetry, the vertex, dilation, and determine if the vertex is a maximum or a minimum then find the value.
Vertex: (3, -4)
Axis of symmetry: x = 3
Min = - 4
Dilation: 1
y-intercept: (0, 5)
x-intercept(s): (1, 0) and (5, 0)
200
Convert the following equation to standard form.
y = (2m + 3)(4m - 3)
y = 8m2 + 6m - 9
200
Convert the following equation to vertex form.
y = n2 - 4n - 60
y = (x - 2)2 - 64
200
Convert the following equation to factored form.
y = x2 - 7x - 30
y = (x + 3)(x - 10)
300
Given the following equation, name the vertical shift AND horizontal shift of the parabola from the parent graph.
y = -1/3(x - 5)2 - 8
Horizontal Shift right 5 and Vertical shift down 8
300
Given the following features, write the factored form of the parabola.
Vertex: (4. -2)
Axis of symmetry: x = 4
Min = -2
Dilation: 3
y-intercept: (0, 7)
x-intercept(s): (8, 0) and (-3, 0)
y = 3(x - 8)(x + 3)
300
Convert the following equation to standard form.
y = (x + 2)2 - 4
y = x2 + 4x
300
Convert the following equation to vertex form.
y = x2 - 20x + 97
y = (x - 10)2 - 3
300
Convert the following equation to factored form.
y = x2 - 5x - 24
y = (x - 8)(x + 3)
400
Given the following graph, name ALL the transformations of the parabola from the parent graph.
Reflection, Dilation narrower by 3, horizontal shift left 6, vertical shift down 4
400
Given the following features, write the vertex form of the parabola.
Axis of symmetry: x = -5
Max = 8
Dilation: 1/4
y = -1/4(x + 5)2 + 8
400
Convert the following equation to standard form.
y = - (x + 7)2 - 10
y = - x2 - 14x - 59
400
Convert the following equation to vertex form.
y = 10x2 + 20x - 30
y = 10(x + 1)2 - 40
400
Convert the following equation to factored form.
y = 4x2 + 31x + 21
y = (x + 7)(4x + 3)
500
Given the following equation, name ALL the transformations of the parabola from the parent graph.
y = -1/2(x - 6)2 + 4
Reflection, Dilation wider by 1/2, horizontal shift right 6, and vertical shift up 4
500
Given the following features, write the standard form of the parabola.
Vertex: (-1.5, 101.25)
Axis of symmetry: x = -1.5
Max = 101.25
Dilation: 5
y-intercept: (0, 90)
x-intercept(s): (-6, 0) and (3, 0)
y = -5x2 - 15x + 90
500
Convert the following equation to standard form.
y = -9(x + 9)2 - 2
y = -9x2 - 162x - 731
500
Convert the following equation to vertex form.
y = 3n2 - 12n - 63
y = 3(n - 2)2 - 75
500
Convert the following equation to factored form.
y = 8a2 - 22a + 5
y = (2a - 5)(4a - 1)