
Ashton F.
asked 04/27/21Identify the effect on the graph by replacing A, H and K with a number other than 0 or 1
- Explanation of the transformation type and how it is identified in the equation (related to A, B, H or K)
- Equation of an absolute value function that represents the transformation. Explain how your example has been transformed from the parent function
- Equation of a quadratic function that represents the transformation. Explain how your example has been transformed from the parent function
1 Expert Answer
LeighAnne D. answered 05/01/21
Licensed High School Math Educator with 15 years teaching experience.
BACKGROUND INFO:
1) First you must know what parent functions are. These are the most basic equations that would be graphed at the origin (0,0) with no movement.
Parent functions:
y= x Linear (straight line)
y = x2 Quadratic (u shaped parabola)
y = | x | Absolute Value (v- shaped)
2) Next you must know where a, h, k appear in the equations.
- a will always be BEFORE the x value
- h will come after the a value and will be either inside parenthesis or absolute value signs
- k will be at the end of equation
y = a(x + h)2 +k QUADRATIC
y = a | x + h | + k ABSOLUTE VALUE
3) Now we can look at what effects a,h, and k have on a function.
Positive or Negative functions (a values):
- When the function is Negative you have a REFLECTION over the x -axis. This means your graph opens down or "upside down".
- When the function is Positive, the graph opens up so there is NO reflection.
A Values:
a values effect the SIZE of the graphed function.
- They have a scale factor
- When a is GREATER than 1 (like 1.5, 6, etc) you have a Vertical Stretch [appears taller] & a Horizontal Compression [appears thinner]
- When a is BETWEEN 0 and 1 (a fraction or decimal) you have a Vertical Compression [appears shorter] and a Horizontal Stretch [appears wider].
H Values:
- h values cause left or right movement of the graph. This is called a horizontal shift or TRANSLATION.
- When h is NEGATIVE, the graph moves RIGHT
- When h is POSITIVE, the graph moves LEFT.
K Values
- k values cause up and down movement. This is called a vertical shift or TRANSLATION.
- When k is POSITIVE, the graph moves UP
- When k is NEGATIVE, the graph moves down.
Without having a graph to accompany your question, I cannot be exactly sure what you are asking, but here are some examples.
4) Transformation of Absolute Value Function
Example 1:
y = | x -4 | - 3
- The function is POSITIVE . It opens UPWARD so there is NOT a reflection.
- a = 1 (because there IS no number in front). So there is no change to the size of the graph.
- h = -4 There is a horizontal shift (translation) 4 units to the RIGHT.
- k = -3 There is a vertical shift (translation) 3 units DOWN.
Example 2:
y = - 2| x + 3 | + 4
- a has a negative value. This function is NEGATIVE. It will open down so there is REFLECTION over the x - axis.
- a = 2 This graph will be VERTICALLY STRETCHED & HORIZONTALLY COMPRESSED by a scale factor of 2.
- h = 3. There is a horizontal shift 3 units to the LEFT.
- k = 4. There is a vertical shift 4 units UP.
5) Transformation of Quadratic function
Example: y = - 1/4( x - 5)2 + 1
- a has a negative value. The parabola will open down so there is a REFLECTION across the x- axis.
- a = 1/4. This is a FRACTION. This graph will be VERTICALLY COMPRESSED and HORIZONTALLY STRETCHED by a scale factor of 1/4 (or 0.25).
- h = -5. There will be a HORIZONTAL SHIFT 5 units to the RIGHT.
- k = 1. There will be a VERTICAL SHIFT 1 unit up.
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Mark M.
Where is the graph?04/27/21