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Cogito

Algebra 1 · Chapter 8 · Lesson 3

Practice Worksheet

The Discriminant

How many real roots, before solving.

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

NameDate

Figure — use these to answer the problems

Move the parabola up and down and watch the number of crossings change.
-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.

4 problems

  1. a = 1, b = 2, c = 1. Discriminant?

    Answer

  2. a = 1, b = 4, c = 4. Discriminant?

    Answer

  3. Discriminant 0. How many real roots?

    Answer

  4. a = 1, b = 1, c = 5. Discriminant?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Discriminant −19. How many real roots?

    Answer

  2. a = 2, b = 5, c = 2. Discriminant?

    Answer

  3. Sort each discriminant by the number of real roots it gives.

    Write each item under the heading it belongs to: Positive · Zero · Negative

    Two roots

    One root

    No real roots

Stretch Yourself

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

4 problems

  1. A parabola touching the axis exactly once. Discriminant?

    Answer

  2. a = 1, b = 0, c = −9. Discriminant?

    Answer

  3. The Value

    a = 1, b = 6, c = 5. What is the discriminant?

    Answer

  4. The Count

    Discriminant 16. How many real roots?

    Answer