Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Algebra 2 · Chapter 1 · Lesson 1

Practice Worksheet

Shifting, Stretching, and Reflecting

One set of rules for every curve.

8 problems · about 20 minutes · F-BF.B.3, F-IF.C.7

NameDate

Figure — use these to answer the problems

Shift the vertex sideways and up, and stretch the arms.
-8-8-6-6-4-4-2-222446688
y = 1|x + 0| + 0
Vertical stretch a1
Shift right by0
Shift up by0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. y = (x − 6)² − 2. Vertex x-coordinate?

    Answer

  2. Why does f(x − 3) shift the graph right?

    • x must be 3 bigger to give the same output.
    • Because that is the rule.

  3. y = (x + 5)². Vertex x-coordinate?

    Answer

  4. y = (x − 2)² + 6. Vertex y-coordinate?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. y = −x². Does it open up or down?

    • Down.
    • Up.

  2. y = 3x². Is it narrower or wider than y = x²?

    • Narrower.
    • Wider.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Shift

    y = (x − 4)². What is the x-coordinate of the vertex?

    Answer

  2. The Lift

    y = x² + 7. What is the y-coordinate of the vertex?

    Answer