# Algebra 2 Unit 3 Flashcards

1
Q

The Absolute Value parent function is…

A

f(x) = |x|

2
Q

What is a Piecewise Function?

A

A piecewise function is made up of 2 or more functions, each with its own domain

3
Q

When graphing Absolute Value Inequalities, NOT equal to means to graph the line as a ________ line.

A

Dotted

4
Q

Give a brief description of what to do… f(x) = |x| - 2

A

Shift the parent function two units down

5
Q

Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = - x^2 +6x

A

Maximum because “a” is negative, AOS is x = 3 (Use x = -b/a), Vertex is (3,9) Plug the x into equation to find the y-value

6
Q

The Square Root parent function is…

A

f(x) = square root of x

7
Q

What is the standard form of the quadratic function?

A

y = ax^2 + bx +c

8
Q

When a > 1, then the parent functions dilations is a vertical…

A

Stretch or becomes skinny like a rubber band is being pulled up to down

9
Q

Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = x^2 - 8x + 9

A

Minimum, AOS is x = 4, Vertex is 4, -7)

10
Q

What is the generic formula for the Axis of Symmetry(AOS)?

A

x = h

11
Q

What is the end behavior of any polynomial function?

A

The behavior of the graph of f(x) as x approaches positive infinity or negative infinity

12
Q

When the parent function is negative in front of the a value, then the entire parent function…

A

Reflects or Flips upside down

13
Q

Describe the Tranformation of f(x) = - 5/4 (x + 6) - 7

A

Reflects over the x-axis, stretches by 5/4, shifts left 6 units, shifts down 7 units

14
Q

The turning point of a parabola is called the…

A

Vertex

15
Q

Give a brief description of what to do… f(x) = - |x|

A

Reflect the parent function over the x-axis (flip upside down)

16
Q

What is the Axis of Symmetry Formula (AOS)?

A

x = - b over 2a

17
Q

A Qyadratic Function creates a U-shaped curve called a …

A

Parabola

18
Q

What does the two lined R symbol stand for?

A

All Real Numbers

19
Q

What is the Vertex of an Absolute Vale Function?

A

(h,k)

20
Q

When given a quadratic function, when a is positive, the function will ________, creating a __________.

A

Up creating a Minimmum

21
Q

Why might someone prefer the vertex form over the standard form of a quadratic function?

A

The vertex form literally gives the vertex

22
Q

When graphing Absolute Value Inequalities, greater than means to shade ________.

A

Above

23
Q

Describe the Tranformation of f(x) = 2/3 (x - 3) + 2

A

Compression by 2/3, Shifts right 3, Shifts up 2

24
Q

What do you call the line that divides a parabola into two equal sections?

A

The Axis of Symmetry

25
Q

Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = 4x^2

A

Minimum, AOS is x = 0, Vertex is (0,0)

26
Q

When the vertex is at its highest point, it’s called a …

A

Maximum

27
Q

Describe the Tranformation of f(x) = - (x + 9)

A

Reflects over the x-axis, shifts left 9 units

28
Q

The Logarithmic parent function is…

A

f(x) = log x

29
Q

What are the 5 steps to convert from Standard form to Vertex form when given a Quadratic Function?

A

1) Group ax^2 + bx 2) If a does not equal 1, factor it outside so it becomes a(x^2 +bx) 3) Complete the square 4)Subtract AC from the end of the equation 5)Factor the Trinomial and Simplify the equation

30
Q

Give a brief description of what to do… f(x) = 1/2|x|

A

Vertical Compression by 1/2 (Becomes Wide)

31
Q

The “c” in the quadratic function is called the…

A

Constant or y-intercept

32
Q

Describe the Tranformation of f(x) = 4 (x) - 4

A

Stretches by 4, shifts down 4 units

33
Q

Give a brief description of what to do… f(x) = 2|x|

A

Vertical Stretch by 2 (Becomes Skinny)

34
Q

A

f(x) = x squared or x^2

35
Q

When graphing Absolute Value Inequalities, less than means to shade ________.

A

Below

36
Q

When given a quadratic function, when a is negative, the function will ________, creating a __________.

A

Down creating a Maximum

37
Q

When the vertex is at its lowest point, it’s called a …

A

Minimum

38
Q

Give a brief description of what to do… f(x) = |x| + 2

A

Shift the parent function two units up

39
Q

When translating a function, (x) + k means to…

A

Shift up “k” units

40
Q

Give a brief description of what to do… f(x) = |x + 2|

A

Shift the parent function two units left

41
Q

When a < 1, then the parent functions dilations is a vertical…

A

Compression or becomes wide like a rubber band is being pulled from left to right

42
Q

Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = - 2x^2 + 7

A

Maximum, AOS is x=0, Vertex is (0.7)

43
Q

The Cubic parent function is…

A

f(x) = x cubed or x^3

44
Q

When translating a function, (x - h) means to…

A

Shift right “h” units

45
Q

Give a brief description of what to do… f(x) = |x - 2|

A

Shift the parent function two units right

46
Q

What is the Vertex Form of an Absolute Vale Function?

A

f(x) = a |x - h| + k

47
Q

When translating a function, (x + h) means to…

A

Shift left “h” units

48
Q

The Cubic parent function is…

A

f(x) = cubic root of x

49
Q

The Reciprocal parent function is…

A

f(x) = 1 over x

50
Q

When graphing Absolute Value Inequalities, equal to means to graph the line as a ________ line.

A

Solid

51
Q

The Exponential parent function is…

A

f(x) = 2 to the x power

52
Q

The Linear parent function is…

A

f(x) = x

53
Q

When translating a function, (x) - k means to…

A

Shift down “k” units