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Cogito

Algebra 1 · Chapter 8 · Lesson 1

Practice Worksheet

Parabolas and Their Roots

What the graph tells you about the solutions.

10 problems · about 20 minutes · F-IF.C.7, A-REI.B.4, A-APR.B.3

NameDate

Figure — use these to answer the problems

Move the curve until it crosses the axis twice, then once, then not at all.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x − 4
  • Point(2, 0)
a1
b0
c-4
Read at x2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Factoring Quadratic Trinomials”

    Multiply to 18, add to 9. Larger number?

    Answer

  2. From “Multiplying and Factoring”

    x² + 11x + 24 = (x + 3)(x + ?). Missing number?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

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

    Answer

  2. What do the roots of a quadratic correspond to on its graph?

    • Where it crosses the x-axis.
    • The turning point.

  3. x² − 9 = 0. What is the positive root?

    Answer

  4. (x − 1)(x − 6) = 0. What is the larger root?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. y = x² − 8x + 3. x-coordinate of the vertex?

    Answer

  2. x² + 5x + 6 = 0. What is the larger root?

    Answer

Stretch Yourself

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

2 problems

  1. The Roots

    (x − 4)(x − 7) = 0. What is the larger root?

    Answer

  2. The Vertex

    y = x² − 6x + 5. What is the x-coordinate of the vertex?

    Answer