Skills · Quadratics · Solving Quadratics
The quadratic formula
Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.
Problem types
- x² + bx + c = 0, whole answers: x² − 5x + 6 = 0
- ax² + bx + c = 0, a past 1: 2x² + 3x − 2 = 0
- a radical answer: x² − 4x + 1 = 0
- not in standard form (rewrite first): x² = 3x + 4
- no real solution: x² + x + 5 = 0
Sample Sheet · Level 1
- x² − 3x − 40 = 0
- x² − 10x + 21 = 0
- x² − 16x + 63 = 0
- x² + 6x − 27 = 0
- x² + 9x + 14 = 0
- x² + x − 72 = 0
- x² − 11x + 28 = 0
- x² − 4x − 5 = 0
Answer key
- x = −5 or x = 8
- x = 3 or x = 7
- x = 7 or x = 9
- x = −9 or x = 3
- x = −7 or x = −2
- x = −9 or x = 8
- x = 4 or x = 7
- x = −1 or x = 5
Sample Sheet · Level 3
- 4x² + 16x + 7 = 0
- 4x² − 20x + 21 = 0
- x² + 4x − 9 = 0
- x² + 9x − 22 = 0
- 2x² + 3x + 12 = 0
- x² + x − 6 = 0
- x² = 15x − 44
- x² = −17x − 72
Answer key
- x = −72 or x = −12
- x = 32 or x = 72
- x = −2 ± √13
- x = −11 or x = 2
- no real solution
- x = −3 or x = 2
- x = 4 or x = 11
- x = −9 or x = −8
Make your own
Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.