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Cogito

Integrated Math 2 · Chapter 2 · Lesson 3

Practice Worksheet

Systems With a Quadratic

Where a line meets a curve.

12 problems · about 21 minutes · A-REI.C.7

NameDate

Figure — use these to answer the problems

Raise and lower the parabola. Compared with a fixed horizontal line, it can cross twice, touch once, or miss.
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y = 1x² + 0x − 3
a1
c, vertical position-3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y = x² and y = 16. What is the positive x value?

    Answer

  2. What does exactly one solution mean geometrically?

    • The line touches the parabola without crossing it.
    • The line is parallel to the parabola.

  3. y = x² and y = 4. What is the positive x value?

    Answer

  4. y = x² and y = 9. Positive x value?

    Answer

  5. y = x² and y = 0. How many intersection points?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y = x² and y = −4. How many intersection points?

    Answer

  2. y = x² and y = 2x. What is the non-zero x value?

    Answer

  3. y = x² and y = x + 6. What is the smaller x value?

    Answer

Stretch Yourself

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

4 problems

  1. Put the solving process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Substitute the linear equation into the quadratic.
    • Rearrange so one side is zero.
    • Solve the resulting quadratic for x.
    • Substitute each x back to find its y.

  2. y = x² and y = 25. Positive x value?

    Answer

  3. The Intersection

    y = x² and y = x + 6. What is the larger x value?

    Answer

  4. The Matching y

    Same system. What is y when x = 3?

    Answer