Unit 1 - Transformations
Which of the following transformations changes an images size?
Translation, reflection, rotation, and dilation
Dilations
Factor: x2 - 10x + 16
(x - 8)(x - 2)
Simplify √125
5√5
(3x2 - 5x + 6) + (2x2 + 3x - 9)
5x2 - 2x - 3
Line AB has a length of 6 units. It's then dilated by a scale factor of 1/2. What is its new length?
3 units
What is the final image of A(2,3) after a rotation of 90 degrees counterclockwise?
A'(-3,2)
Factor: 7x2 + 19x - 6
(7x - 2)(x + 3)
Simplify √40 * √9
6√10
Simplify the imaginary number to its simplest form:
-7i7
7i
What are the solution(s) to the following system?
3x + y = 14
y = x2 - 5x + 1
(-2.74 , 22.225) and (4.742, -0.225)
What is the final image of B(1,5) after a translation of (x + 3, y) and then a rotation of 180 degrees?
B''(-4, -5)
Factor the following using the GCF:
14a3b4c5 + 21a7bc8
7a3bc5(2b3 + 3a4c3)
What is the domain of y = √(3x + 3) - 1
(You can use Desmos)
[-1, ∞ )
The function h(t) = -16t2 + 90t + 20 shows the height of a projectile after it's thrown. What is a realistic domain for this function?
0 to 5.839
Simplify √12 + √192 - √27
7√3
What is the final image of C(8,-2) after a reflection across the x- axis and a dilation of 2?
C''(16,4)
Write in vertex form by completing the square:
y = x2 + 8x + 7
y = (x + 4)2 - 9
Solve for x:
√(x-2) + 1 = x - 4
x = 7.303
What is the angle of rotation to move from 2 to 6 rotating clockwise?
120 degrees
The graph of y= ax2 + c contains the point (0,0). Which point lies on the graph of y = a(x + 3)2 + c?
Shifted 3 to the left : (-3,0)
The point D(3, 7) is reflected over the y-axis and then rotated 90 degrees counterclockwise. What translation would bring it back to the origin (0,0)?
(x + 7, y + 3)
Solve the quadratic: x2 - 2x + 10
x = 1 ± 3i
What is the domain and range of the following:
√(x-2) + 1 =
Domain: [2, ∞ )
Range: [1, ∞ )
Solve using the quadratic formula:
3x2 - 4x - 5 = 0
4 ± √66 / 6
The graph of y= ax2 + c contains the point (0,0). Which point lies on the graph of y = ax2 + 5?
Shifted up 5: (0,5)