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Cogito

Integrated Math 2 · Chapter 2 · Lesson 2

Practice Worksheet

The Quadratic Formula

A method that always works.

12 problems · about 22 minutes · A-REI.B.4

NameDate

Figure — use these to answer the problems

Lift the parabola until it stops touching the axis. That is the moment the discriminant turns negative.
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y = 1x² + 0x − 4
a1
b0
c-4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. x² + 3x + 2 = 0. What is the discriminant?

    Answer

  2. A negative discriminant means what about the graph?

    • The parabola never crosses the x-axis.
    • It crosses twice.

  3. x² − 6x + 5 = 0. Discriminant?

    Answer

  4. Same equation. Larger root?

    Answer

  5. x² − 4x + 4 = 0. Discriminant?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many distinct real roots does that have?

    Answer

  2. x² + x + 3 = 0. Discriminant?

    Answer

  3. How many real roots does that have?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each discriminant by what it predicts.

    Write each item under the heading it belongs to: Discriminant 25 · Discriminant 3 · Discriminant negative 9 · Discriminant negative 1

    Two real roots

    No real roots

  2. 2x² − 8x + 6 = 0. Larger root?

    Answer

  3. The Discriminant

    x² − 4x + 1 = 0. What is the discriminant?

    Answer

  4. The Prediction

    x² + 2x + 5 = 0. What is the discriminant?

    Answer