Cogito
Algebra 2 · Chapter 1 · Lesson 1
Shifting, Stretching, and Reflecting
One set of rules for every curve.
8 problems · about 20 minutes · F-BF.B.3, F-IF.C.7
What this lesson teaches
The student describes and performs transformations of a function from its equation.
- Changes outside the function move it vertically.
- Changes inside move it horizontally, and in the opposite direction.
- A multiplier stretches, and a negative one reflects.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = (x − 6)² − 2. Vertex x-coordinate?
Answer 6
Why 6.
Why does f(x − 3) shift the graph right?
Answer x must be 3 bigger to give the same output.
Why The input must grow to compensate.
y = (x + 5)². Vertex x-coordinate?
Answer -5
Why x + 5 means shift left.
y = (x − 2)² + 6. Vertex y-coordinate?
Answer 6
Why The added constant.
Build It Up
The same ideas with more to keep track of.
2 problemsy = −x². Does it open up or down?
Answer Down.
Why A negative reflects it.
y = 3x². Is it narrower or wider than y = x²?
Answer Narrower.
Why A vertical stretch.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Shift: y = (x − 4)². What is the x-coordinate of the vertex?
Answer 4
Why 4.
The Lift: y = x² + 7. What is the y-coordinate of the vertex?
Answer 7
Why 7.