Graphs in Vertex Form
Transformations
Simplifying
Writing
Solving
100
f(x) = -2(x-3)2 + 4
What is the vertex?
Is it a max/min?
(3, 4)
Max
100
Describe the transformations of g(x) = 3(x + 2)2 - 4 of the graph of f(x) = x2
Reflection, vertical stretch by a factor of 3, translated left 2 and down 4
100
sqrt(-25)
5i
100
Write the function f(x) = x2 that is reflected, and translated up 3 units.
f(x) = -x2 + 3
100
How many solution(s) does the function have according to the graph.
2 real solutions
200
Graph the function f(x) = 1/2(x - 4)2 + 1 be sure to fill in the appropriate table of values
Vertex (4,1)
200
Describe the transformations of the function f(x) =1/2 x2 + 3
Vertical compression by a factor of 1/2, translated 3 units up
200
sqrt140
2sqrt35
200
Write the function f(x) =x2, that is represented by the following transformations:
vertically compressed by a factor of 1/4
translated left 4 units and up 1 unit
f(x) = 1/4(x + 4)2 + 1
200
What does it mean graphically if the function only has one solution?
It means the vertex is on the x-axis.
300
Given the function: f(x) = 3(x - 5)2, state the domain and range.
Domain:(-infinity, infinity) or {All real numbers}
Range: [0, infinity)
300
Write the function f(x) =x2 that is translated left by 2 units and down by 5 units.
f(x) = (x +2)2-5
300
2/ (4i)
-i/2
300
Write the function whose axis of symmetry is at x = 0 with a range of (-infinity, -4]
f(x)= -x2 - 4
300
Draw a graph that has no real solutions.
400
Given the graph of the function, identify the solutions.
x = -3 and x = 1
400
Describe the transformations given the graph:
reflection, left 3, up 1
400
(3-5i)(8+10i)
74-10i
400
Write the function of the graph given the vertex (3, 2) and going through the point (5,14)
f(x) = 3(x-3)2+2
400
Find the solutions to the the function:
f(x) = 3(x - 2)2 + 6
2+2i, 2-2i
500
Given the graph:
Identify the vertex, axis of symmetry, and the range.
State the end behavior
vertex (2,1) max
aos: x = 2
Range: (-inf, 1]
As x-> -inf, f(x) -> -inf.
As x-> inf.,f(x) -> infinity
500
How do the variables a, h and k effect the graph of x2?
-a reflects the graph
|a| > 1 vertical stretch
0<|a|<1 vertical compression
h: horizontal translation (-h, right)(+h, left)
k: vertical translation (+k, up) (-k, down)
500
(7+ 3i)/(6-2i)
(9+8i)/10or 9/10+(4i)/5
500
Write the function given the graph:
f(x) = 1/2(x-4)2-2
500
What are the solutions to the quadratic equation
y=1/2(x - 2)^2 -8
-2, 6