Transformations
Complex Numbers / Quadratics
Circles / Parabolas
Hyperbolas / Ellipses
Matrices
100
Describe how the function is a transformation of the original function f(x).
f(x+10)
Translated left 10 units
100
Subtract 2-5i FROM
4+3i
2+8i
100
Write the standard equation of a circle with a center at (-4, 9) and has a radius of 6.
(x+4)^2+(y-9)^2=36
100
What are the points of the vertices?
(x+11)^2/1+(y+7)^2/25=1
(-11, -2) and (-11, -12)
100
What row operation would allow you to get a 0 in row 2 column 1?
R2=R2-4R1
200
Describe how the function is a transformation of the original function f(x).
3f(x)+13
Vertical stretch by 3 and translated up 13 units
200
Multiply
(2-4i)(3+2i)
14-8i
200
What is the focus and directrix of
(x+1)^2=-32(y-4)
Focus: (-1, -4)
Directrix: y= 12
200
Where are the vertices?
(y-3)^2/4-(x+2)^2/5=1
(-2, 5) and (-2, 1)
200
A circle passes through (4, -2), (-1, 3), and (5, 7).
Using the general form of a circle x^2+y^2+Dx+Ey+F=0 and the points above, fill in the missing numbers to create a system of equations.
(4, -2) creates D(__) + E(__) + 1F = (__)
(4, -2) creates D(4) + E(-2) + 1F = (-20)
300
Describe how the function is a transformation of the original function f(x).
f(2x-4)+6
Horizontal compression by 1/2, translated right 2 and up 6.
300
Find the vertex of f(x)=x^2+8x+18
(-4,2)
300
What is the center and radius of the following circle?
x^2+y^2+14x-20y-20=0
Center: (-7, 10)
Radius: 13
300
What is the location of the foci?
9x^2-16y^2-54x+32y-79=0
(8, 1) and (-2, 1)
300
In the process of finding the inverse of the following matrix, explain the indicated row operation.
Step 1: Switch row 1 and row 2.
Answer to step 1: 
Step 2: Explain the row operation to change the answer from step 1 to the result below.
400
Write a formula for f(x)=sqrt(x) reflected over the y-axis, shifted down 9 units and right 1 unit.
f(x)=sqrt(-(x-1))-9
OR
f(-(x-1))-9
400
What are the roots of
f(x)=x^2-4x+5
2+-i
400
Find the equation fo the parabola which has a vertex at (3, 0) and a focus at (0,0)
y^2=-12(x-3)
400
What are the foci points?
2x^2+y^2-12x+14=0
(3, sqrt2) and (3, -sqrt2)
400
Four points on a hyperbola are (-6, 2), (-3, -4), (1, 5), and (4, -2). Use matrices to represent the system of equations using the general form x^2+Cy^2+Dx+Ey+F=0 and all four points, in the order the points are given.
Find the values of a, b, c, d and t.
a = 4
b = -6
c = 2
d = 1
t = -16
500
Write an equation for the transformed parent function.
f(1/3(x-2))+1
1/3abs(x-2)+1
500
Let f(x)=x^2+2x+3
Evaluate f(-1+3i)
-7
500
Find the equation for the parabola which has a focus at (12, 3) and directrix at x=6.
(y-3)^2=12(x-9)
500
What is the standard equation of the hyperbola with a vertex at (-10, 4) and asymptotes at
y=+-3/5(x+5)+4
500
When finding an inverse by hand, the original matrix is written in augmented form.
Start with the augmented matrix above and follow the two row operations below.
This results in
Find all the missing values.
a = -2
b = 1
c = -1
d = -2
e = 2
f = 8
g = -4