Characteristics
f(x)=ax^2
f(x)=ax^2 + c
f(x)=a(x-h)^2 + k
FINAL Jeopardy!
100
Does this graph have a maximum of a minimum?
The Graph has a MAXIMUM.
100
A U-Shaped graph.
A Parabola
100
What is the vertex and transformation of the parabola g(x) shown below:
VERTEX: (0, -2)
VERTICAL TRANSLATION DOWN by 2.
100
in the equation:
f(x) = a(x-h)^2
what happens when h < 0?
If h < 0, The graph HORIZONTALLY SHIFTS to the LEFT.
200
Define the vertex of a quadratic graph.
The LOWEST or the HIGHEST center-most point of the graph.
200
What happens if a < 1 in the function
f(x)=ax^2
The graph VERTICALLY SHRINKS.
200
What is the y-intercept of the function:
f(x)= 3x^2 + 4
Y-Intercept is 4
200
What is the vertex for the function:
f(x) = -2(x-9)^2
VERTEX: (9, 0)
300
What do the (x, y) represent in the Vertex?
The x is the Axis of Symmetry.
the y is either the Maximum of Minimum.
300
What is the vertex for the function:
f(x) = x^2
VERTEX: (0,0)
300
DOUBLE JEOPARDY!!!!
What does c transform on the graph?
It Vertically TRANSLATES the graph UP or DOWN
300
For the equation:
f(x)= 1/2(x+4)^2
What is the Axis of Symmetry and transformation?
AoS: x = -4
HORIZONTALLY SHIFTS to the LEFT by 4 UNITS
500
DOUBLE JEOPARDY!!!!!
What are the transformations for the graph f(x)?
The graph REFLECTS over the x-axis and VERTICALLY SHRINKS by
1/3
500
In
f(x) = ax^2
, if the number a > 1, what happens to the graph?
The graph VERTICALLY STRETCHES.
500
What is the Vertex of the function:
f(x) = -x^2 - 16
VERTEX: (0, -16)
500
DOUBLE JEOPARDY!!!
What is the vertex and transformation of the following function:
f(x)= (x+10)^2 + 12
VERTEX: (-10, 12)
HORIZONTAL TRANSLATION 10 UNITS to the LEFT and a VERTICAL TRANSLATION 12 UNITS UP.
1000
What is the vertex, axis of symmetry, minimum/maximum, domain and range of the following function:
Vertex: (2, -3)
AoS: x = 2
Minimum: y = -3
Domain: ALL REAL NUMBERS
Range: y ≥ -3
1000
What are the transformations of the function?
f(x)= -1/2 x^2
The graph REFLECTS over the x-axis and vertically SHRINKS.
1000
Explain the transformation, vertex, Axis of Symmetry, minimum/maximum and give the domain & range of the function:
f(x) = -2x^2 - 8
f(x) REFLECTS over the x-axis and VERTICALLY STRETCHES by 2 and VERTICALLY TRANSLATES DOWN by 8 Units.
Vertex: (0, -8)
Axis of Symmetry: 0
Maximum: y = -8
Domain: ALL REAL NUMBERS
Range: y ≤ -8
1000
For the function:
f(x) = -3(x- 6)^2-7
Give the following:
Transformation, Vertex, Axis of Symmetry, Maximum/Minimum, Domain & Range
REFLECTS over the x-axis and VERTICALLY STRETCHES by 3. HORIZONTAL TRANSLATION by 6 UNITS to the RIGHT. And a VERTICAL TRANSLATION DOWN by 7 UNITS.
Vertex: (6, -7)
AoS: x = 6
Maximum: y = -7
Domain: ALL REAL NUMBERS
Range: y ≤ -7
2000
FINAL JEOPARDY
WRITE DOWN HOW MANY POINTS YOU WANT TO BID ALONG WITH YOUR ANSWER.
You will have 120 seconds to figure out your answer.
What is the equation for the graph. Write it in the form below:
f(x) = a(x-h)^2 + k
f(x) = y = −(x + 1)^2 − 3