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Cogito

Algebra 1 · Chapter 8 · Lesson 2

Practice Worksheet

Completing the Square and the Formula

Where the formula comes from.

10 problems · about 22 minutes · A-REI.B.4, A-SSE.B.3

NameDate

Figure — use these to answer the problems

Make the discriminant negative and watch the curve lift clear of the axis.
-8-8-6-6-4-4-2-222446688
y = 1x² − 4x + 3
a1
b-4
c3
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Parabolas and Their Roots”

    x² − 7x + 12 = 0. What is the larger root?

    Answer

  2. From “Factoring Quadratic Trinomials”

    Multiply to 18, add to 9. Larger number?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. x² − 2x − 8. What is b² − 4ac?

    Answer

  2. A negative discriminant means what?

    • No real roots; the parabola misses the axis.
    • Two roots.

  3. x² + 8x + ? completes the square. What number?

    Answer

  4. x² + 10x + ? completes the square. What number?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. x² − 6x + 9. What is b² − 4ac?

    Answer

  2. x² + 3x + 1. What is b² − 4ac?

    Answer

Stretch Yourself

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

2 problems

  1. The Discriminant

    x² − 4x + 3. What is b² − 4ac?

    Answer

  2. How Many Roots

    x² + 2x + 5. What is b² − 4ac?

    Answer