Show:
Types of
Transformations.
What transformation happened?
Factoring.
Solutions of Equations & Inequalities.
Circles & other things.
100

What transformation does the "h" in the equation describe?

y=(x-h)2+k

Translation: shift left or right.

100

What two transformations happened to f(x) to get

h(x) = -3 f(x)

reflect over x-axis

stretch by factor of 3

100

factor the binomial:

20x2 - 36x

4x(5x-9)

100

Find the solutions to the equation

2x(4x + 1)(x - 3)

show your answer in set notation

hint: {the braces}

{-1/4, 0, 3}

100

What does (h, k) represent for a circle in the equation

(x-h)2 + (y-k)2 = r2

the ordered pair of the center

200

What transformation does the equation describe?

-f(x)

*in other words, the y becomes negative*

Reflection: over the x-axis

200

What two transformations happened to f(x) = x2 to get

h(x) = (x-7)2 + 2

shift right 7 units 

shift up 2 units

200

factor the trinomial

4x2 + 4x - 15

(2x - 3)(2x + 5) 

200

find the solutions of the inequality

x2 + 2x -3 < 0

show your answer in set builder notation or a number line

{x| -3 < x < 1, where x is a Real number}

number line includes -3 and 1 

not shaded circles

shaded between -3 and 1

200

what is the center of the circle whose equation is

(x+3)2 + (y-6)2 = 9

(-3, 6)

300

What transformation does the "k" in the equation describe?

y=(x-h)2+k

Translation: shift up or down

300

what two transformations happened to f(x) = |x| to get

h(x) = 1/2 |x| - 4

compression by factor of 1/2

shift down 4 units

300
factor the trinomial

10x2 + 13x - 30

(5x - 6)(2x + 5)

300

find the solutions to the inequality

2x2 - 4x - 8 ≥  10x - 8

show your answer in set builder notation or a number line

{x| x≤0 or x≥7}

shade 0 and 7

shade left of 0 and right of 7

300

what is the equation of a circle with center (2, 7) and radius 10

(x-2)2 + (y-7)2 = 100

400

What transformation does the equation describe?

f(-x)

*in other words, the x becomes negative*

Reflection: over the y-axis

400

what two transformations happened to f(x) = x2 to get 

h(x) = -(x+5)2

reflect over x-axis

shift left 5 units

400

factor the trinomial

2x2 + 20x + 50

2(x + 5)(x - 5)

400

solve the quadratic equation

x2 + 3x - 14 = -2x + 10

write your answer in set notation

{hint: braces}

{ -8, 3 }

400

What is the center and radius of the circle given by the equation

x2 + y2 = 144

center: (0,0)

radius: 12

500

What transformation does the equation describe?

h(x) = k * f(x)

*bonus points if you have the two specific types

Dilation

*BONUS: if k > 1 is a vertical stretch. if 0 < k < 1 is a vertical compression.

500

what transformations happened to get

h(x) = 4(-x-3)+6

stretch by factor of 4

reflect over y-axis

shift right 3 units

shift up 6 units

500

Factor by completing the square

x2 - 6x + 2

(x - 3)2 - 7

500

Find the solutions to the inequality

|x| ≤  x + 8

show your answer in either set builder notation or a number line

{x | x ≥  -4}

shade to the right of -4

500

What is the center and radius of the circle given the equation

x2 + 10x + y2 - 2y = 10

hint: you will need to factor by completing the square.

equation: (x+5)2 + (y-1)2 = 36

center: (-5, 1)

radius: 6