Quadratic inequalities GCSE lesson: sketch the curve, read off one or two inequalities

Quadratic inequalities: practice

Sketch each curve through its roots and show your working on paper. Test a number in each piece. The stretch is optional.

Diagnostic question: choose and explain

1. Solve x² > 49.
   1. x < −7 or x > 7
   2. x > 7
   3. −7 < x < 7
   4. −7 > x > 7

Practice questions

1. x² < 36, so ___ < x < ___
2. (x − 1)(x − 6) ≤ 0, so ___ ≤ x ≤ ___
3. x² − 4x − 12 > 0, so x < ___ or x > ___
4. x² ≥ 6x, so x ≤ ___ or x ≥ ___
5. Which values of x satisfy x² < −4?
   1. None: x² is never negative
   2. −2 < x < 2
   3. x < −2 or x > 2
6. Zara writes the answer to x² − 1 > 0 as −1 > x > 1. What is wrong?
   1. No number is below −1 and above 1 at once: write x < −1 or x > 1
   2. Nothing: it is right
   3. It should be −1 < x < 1
7. How many integers satisfy x² − 3x − 10 < 0?
8. 2x² + 5x − 3 > 0, so x < ___ or x > ___
9. Stretch: 6 + x − x² > 0, so ___ < x < ___

Support: For question 3: factorise x² − 4x − 12, sketch the curve through its roots, then ask where it is above the axis. How many pieces?

Quadratic inequalities: exit

Show your working and your sketch; one sentence for the last part.

1. Solve x² − x − 12 ≥ 0. Sketch the curve, and say in one sentence why your answer is one inequality or two.

Exit check

One inequality solved and one sentence show who reads the sketch rather than a rule.

Solve x² − x − 12 ≥ 0 and sketch the curve through its roots.

Quadratic inequalities: sketch and read off

Sketch each curve through its roots before you write the answer. Test one number in each piece of your answer.