The Quadratic Formula · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The Quadratic Formula

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. In 2x squared + x - 8 = 0, what is the value of b squared - 4ac?

    Answer: ______________

  2. Which equation is the formula the right tool for, because factorising with whole numbers will not work?

    • x squared - 4x - 2 = 0
    • x squared - 5x + 6 = 0
    • x squared - 7x + 12 = 0
    • x squared + 2x = 0

  3. In 4x squared - 5x + 6 = 0, what value of b goes into the formula?

    • 5
    • -5
    • -6
    • 6

  4. In 5x squared + 2x - 9 = 0, what is 2a, the number that goes on the bottom of the formula?

    • 5
    • 10
    • 2
    • -9

  5. Solve 2x squared - 3x - 1 = 0 with the formula. What is the exact form of the larger root?

    • (3 plus root 17) / 2
    • (3 plus root 17) / 4
    • (3 plus root 34) / 4
    • (3 plus root 17) / 8

  6. Maya solves x squared + 6x + 2 = 0 with the formula and writes x = (-6 plus/minus root 12) / 2. Where did she go wrong?

    • She used b instead of -b
    • She divided by a instead of 2a
    • She worked out the number under the root wrongly
    • She took only the positive root

  7. Solve x squared - 4x - 2 = 0 with the formula. What is the exact form of the larger root?

    • 2 plus root 6
    • 2 plus 2 root 3
    • 4 plus root 6
    • 4 plus 2 root 6

  8. Priya solves x squared + 2x - 3 = 0 with the formula and writes x = (-2 plus/minus root 16) / 2. Her substitution is correct.

    Circle one:   True   False

  9. Solve 2x squared - 5x + 1 = 0 with the formula. Give the smaller root to 2 decimal places.

    • 0.22
    • 2.28
    • -0.22
    • 0.88

  10. Solve x squared - 5x + 3 = 0 with the formula. Give the larger root to 2 decimal places.

    Answer: ______________

LightMySky · lightmysky.comW1-mt_C-4brnRYHY-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

The Quadratic Formula W1-mt_C-4brnRYHY-s1

  1. 65 · b squared is 1 and 4ac is -64, so 1 - (-64) is 65.
  2. x squared - 4x - 2 = 0 · x squared - 4x - 2 has no whole-number pair multiplying to -2 and adding to -4, so factorising fails and the formula is the right tool. The other three factorise: (x - 2)(x - 3), (x - 3)(x - 4), and x(x + 2).
  3. -5 · b is the coefficient of the x term, with its sign attached, so b is -5.
  4. 10 · a is the coefficient of x squared, which is 5, so 2a is 10.
  5. (3 plus root 17) / 4 · The formula gives (3 plus/minus the root of 17) / 4, and 17 is not a square, so the larger root stays as (3 plus root 17) / 4.
  6. She worked out the number under the root wrongly · Her -b is -6 and her bottom is 2, both correct. But b squared - 4ac is 36 - 8, which is 28, not 12.
  7. 2 plus root 6 · The formula gives (4 plus/minus the root of 24) / 2, the root of 24 is 2 root 6, and dividing both terms by 2 gives 2 plus or minus root 6.
  8. True · b is 2 so -b is -2, b squared - 4ac is 4 + 12 which is 16, and 2a is 2. Every part matches.
  9. 0.22 · The formula gives (5 plus/minus the root of 17) / 4, the root of 17 is about 4.123, so the smaller root is 0.877 / 4, about 0.22.
  10. 4.3 · The formula gives (5 plus/minus the root of 13) / 2, the root of 13 is about 3.606, so the larger root is 8.606 / 2, about 4.30.
Worksheet · LightMySky