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Cogito

Algebra 2 · Chapter 2 · Lesson 3

Practice Worksheet

The Quadratic Formula and the Discriminant

One formula, and a number that predicts the answer.

12 problems · about 22 minutes · A-REI.B.4, N-CN.C.7

NameDate

Figure — use these to answer the problems

Lift the parabola until it stops crossing the axis. That is the moment the discriminant turns negative.
-8-8-6-6-4-4-2-222446688
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.
    • The parabola crosses twice.

  3. x² − 6x + 5 = 0. Discriminant?

    Answer

  4. x² − 6x + 5 = 0. The larger root?

    Answer

  5. x² + 2x + 10 = 0. Discriminant?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x² − 10x + 25 = 0. How many distinct real roots?

    Answer

  2. 2x² − 4x − 6 = 0. The larger root?

    Answer

  3. x² + 9 = 0. One root is 3i. What is the other, as a coefficient of i?

    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: b² − 4ac = 25 · b² − 4ac = 0 · b² − 4ac = −9 · b² − 4ac = 3

    Two real roots

    One repeated root

    Two complex roots

  2. x² − 2x + 5 = 0. One root is 1 + 2i. What is the real part of the other root?

    Answer

  3. The Predictor

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

    Answer

  4. The Ball

    A ball follows h = −5t² + 20t. At what time, in seconds, does it return to the ground, other than t = 0?

    Answerseconds