Algebra 2 Unit 3 Flashcards
The Absolute Value parent function is…
f(x) = |x|
What is a Piecewise Function?
A piecewise function is made up of 2 or more functions, each with its own domain
When graphing Absolute Value Inequalities, NOT equal to means to graph the line as a ________ line.
Dotted
Give a brief description of what to do… f(x) = |x| - 2
Shift the parent function two units down
Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = - x^2 +6x
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
The Square Root parent function is…
f(x) = square root of x
What is the standard form of the quadratic function?
y = ax^2 + bx +c
When a > 1, then the parent functions dilations is a vertical…
Stretch or becomes skinny like a rubber band is being pulled up to down
Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = x^2 - 8x + 9
Minimum, AOS is x = 4, Vertex is 4, -7)
What is the generic formula for the Axis of Symmetry(AOS)?
x = h
What is the end behavior of any polynomial function?
The behavior of the graph of f(x) as x approaches positive infinity or negative infinity
When the parent function is negative in front of the a value, then the entire parent function…
Reflects or Flips upside down
Describe the Tranformation of f(x) = - 5/4 (x + 6) - 7
Reflects over the x-axis, stretches by 5/4, shifts left 6 units, shifts down 7 units
The turning point of a parabola is called the…
Vertex
Give a brief description of what to do… f(x) = - |x|
Reflect the parent function over the x-axis (flip upside down)
What is the Axis of Symmetry Formula (AOS)?
x = - b over 2a
A Qyadratic Function creates a U-shaped curve called a …
Parabola
What does the two lined R symbol stand for?
All Real Numbers
What is the Vertex of an Absolute Vale Function?
(h,k)
When given a quadratic function, when a is positive, the function will ________, creating a __________.
Up creating a Minimmum
Why might someone prefer the vertex form over the standard form of a quadratic function?
The vertex form literally gives the vertex
When graphing Absolute Value Inequalities, greater than means to shade ________.
Above
Describe the Tranformation of f(x) = 2/3 (x - 3) + 2
Compression by 2/3, Shifts right 3, Shifts up 2
What do you call the line that divides a parabola into two equal sections?
The Axis of Symmetry
Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = 4x^2
Minimum, AOS is x = 0, Vertex is (0,0)
When the vertex is at its highest point, it’s called a …
Maximum
Describe the Tranformation of f(x) = - (x + 9)
Reflects over the x-axis, shifts left 9 units
The Logarithmic parent function is…
f(x) = log x
What are the 5 steps to convert from Standard form to Vertex form when given a Quadratic Function?
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
Give a brief description of what to do… f(x) = 1/2|x|
Vertical Compression by 1/2 (Becomes Wide)
The “c” in the quadratic function is called the…
Constant or y-intercept
Describe the Tranformation of f(x) = 4 (x) - 4
Stretches by 4, shifts down 4 units
Give a brief description of what to do… f(x) = 2|x|
Vertical Stretch by 2 (Becomes Skinny)
The Quadratic parent function is…
f(x) = x squared or x^2
When graphing Absolute Value Inequalities, less than means to shade ________.
Below
When given a quadratic function, when a is negative, the function will ________, creating a __________.
Down creating a Maximum
When the vertex is at its lowest point, it’s called a …
Minimum
Give a brief description of what to do… f(x) = |x| + 2
Shift the parent function two units up
When translating a function, (x) + k means to…
Shift up “k” units
Give a brief description of what to do… f(x) = |x + 2|
Shift the parent function two units left
When a < 1, then the parent functions dilations is a vertical…
Compression or becomes wide like a rubber band is being pulled from left to right
Find the Min/Max, AOS, and Vertex of this Quadratic Function…f(x) = - 2x^2 + 7
Maximum, AOS is x=0, Vertex is (0.7)
The Cubic parent function is…
f(x) = x cubed or x^3
When translating a function, (x - h) means to…
Shift right “h” units
Give a brief description of what to do… f(x) = |x - 2|
Shift the parent function two units right
What is the Vertex Form of an Absolute Vale Function?
f(x) = a |x - h| + k
When translating a function, (x + h) means to…
Shift left “h” units
The Cubic parent function is…
f(x) = cubic root of x
The Reciprocal parent function is…
f(x) = 1 over x
When graphing Absolute Value Inequalities, equal to means to graph the line as a ________ line.
Solid
The Exponential parent function is…
f(x) = 2 to the x power
The Linear parent function is…
f(x) = x
When translating a function, (x) - k means to…
Shift down “k” units
