Transformations
Maximum/Minimum
Key Attributes of Quadratic Functions
Domain and Range of Quadratic Functions
Vertex form/standard form
Graphing
100
List the 3 transformations for y = -3 ( x +1 )2
1. Shift left 1
2. Vertical stretch by factor of 3
3. Reflect over x-axis
100
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -2(x-1)2+3
max= 3
100
A parabola has a vertex of (2,-11). What is the equation of the axis of symmetry?
x = 2
100
What is the domain of f(x) =5x2 - 6x +3?
All real numbers
100
Given the vertex of ( -2,5 ) and a point ( 0,1),
what is the quadratic equation in vertex form?
y = - ( x +2 )2 +5
100
Sketch the graph of: y = x2 + 3
200
List 4 transformations for y=-1/2 ( x - 5 )2 -1
1. H. Shift down 1.
2. V. Shift right 5.
3. Vertical compression by factor of 1/2.
4. Reflect over x-axis.
200
Determine whether this function has a maximum or minimum value, and find that value:
f(x) =3(x+2)2-7
min = -7
200
A quadratic equation of y= -8x2 -32x+9. What is the equation of the axis of symmetry?
x = -1
200
What is the range of f(x) = x2 - 7?
y is greater than or equal to -7
200
Given the vertex of ( -3,-4 ) and a point (1,-6),
what is the quadratic equation in vertex form?
y=-1/8(x+3)2 - 4
200
Sketch the graph of: y = (x - 4)2
300
What is the transformed equation after the parent function has shifted up 4 units and vertically compressed by a factor of 1/3 ?
y = 1/3x2 +4
300
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -4(x+3)2 +6
max = 6
300
What can you say about the graph of the parabola when a<0 and when a>0?
When a<0 , it opens downward.
When a>0, it opens upward.
300
What is the domain of f(x) = -x2?
All real numbers
300
Given the vertex of ( 6,-16 ) and a point ( 3,2),
what is the quadratic equation in vertex form?
y=2(x-6)2 - 16
300
Sketch the graph of: y = (x + 1)2 + 5
400
What is the transformed equation after the parent function has shifted left 8 units and vertically stretch by a factor of 6 ?
y=6(x-8)2
400
Determine whether this function has a maximum or minimum value, and find that value: f(x) = x2 + 12x + 27
min = -9
400
What is the y-intercept of y=-2(x+3)2 +14
(0,-4)
400
What is the range of f(x) = -(x+4)2 + 8?
y is less than or equal to 8
400
Change y=(x-7)2 - 25 to standard form.
y=x2 -14x + 24
400
Sketch the graph of: y = -3(x +6)2
500
What is the transformed equation after the parent function has shifted right 7 units, shifted down 4 units and vertically stretch by a factor of 3 ?
y=3(x-7)2 -4
500
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -2x2 - 8x +5
max=13
500
What is the y-intercept of y =1/3( x-9)2 - 7?
(0,20)
500
What is the range of f(x) =x2 - 2x+ 3
y is greater than or equal to 2.
500
Change y=-4(x+5)2+61 to standard form.
y=x2-40x-39
500
Sketch the graph of: y = -2/5(x -7)2 +4
