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Cogito

Integrated Math 2 · Chapter 1 · Lesson 2

Practice Worksheet

Vertex Form and Transformations

Reading the vertex straight off the equation.

12 problems · about 21 minutes · F-BF.B.3, F-IF.C.8

NameDate

Figure — use these to answer the problems

Change c and the parabola slides vertically. Change b and the vertex moves sideways as well.
-8-8-6-6-4-4-2-222446688
y = 1x² − 6x + 5
a1
b-6
c5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y = (x − 6)² + 1. What is the vertex x-coordinate?

    Answer

  2. Why does y = (x − 3)² have its vertex at x = 3?

    • The bracket is zero there, which is its smallest possible value.
    • It is an arbitrary rule about signs.

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

    Answer

  4. y = (x + 4)² − 1. Vertex x-coordinate?

    Answer

  5. y = (x − 2)² + 7. What is the minimum value?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. To complete the square on x² − 8x, what is added?

    Answer

  2. To complete the square on x² + 10x, what is added?

    Answer

  3. y = −(x − 1)² + 9. What is the maximum value?

    Answer

Stretch Yourself

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

4 problems

  1. Put the completing-the-square steps in order.

    Write 1 to 4 in the boxes to put these in order.

    • Halve the coefficient of x.
    • Square that result.
    • Add and subtract it inside the expression.
    • Write the perfect square and collect the constants.

  2. y = (x − 7)² − 3. Vertex y-coordinate?

    Answer

  3. The Vertex

    y = (x − 3)² − 4. What is the x-coordinate of the vertex?

    Answer

  4. The Minimum

    Same equation. What is the minimum value of y?

    Answer