The quadratic formula can be derived from the general form of a quadratic equation.
It can be derived by completing the square.
The formula is useful when the quadratic cannot be easily factorised.
Technology can be used to identify solutions and is useful for checking.

Common misconception

Mistakes often occur when substituting into the quadratic formula with calculators, as pupils miss out brackets and change the priority of operations.

Values should always be put in brackets when substituted. This avoids mistakes when squaring and subtracting negative values. It also makes it easier to change the values of a , b , and c when working on a new question.

Keywords

Quadratic formula - The quadratic formula is a formula for finding the solutions to any quadratic equation of the form ax^2 + bx + c = 0

The first learning cycle derives the quadratic formula. The slides are animated to allow pupils to think about what they could do next before the next step appears on screen. For the task, you may wish to cut up the steps and allow students to move then round into the correct order.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Using the formula $$3m = 20x + 12y$$, if $$x = 3$$ and $$y = 9$$, what calculation would find $$m$$?

$$\frac{12 \times 3 + 20 \times 9}{3}$$

Correct answer: $$\frac{20 \times 3 + 12 \times 9}{3}$$

$$\frac{20 \times 3 + 12 \times 3}{9}$$

Q2.

Using the formula $$2m = 14x + y$$, if $$x = 8$$ and $$y = 5$$, what calculation would find $$m$$?

Correct answer: $$\frac{14 \times 8 + 5}{2}$$

$$\frac{5 \times 8 + 14}{2}$$

$$\frac{14 \times 8 + 2}{5}$$

Q3.

Using the formula $$x = 3a + t^2$$, if $$a = 5$$ and $$t = 6$$, what calculation would find $$x$$?

$$3 \times 5 + 2^6$$

$$3 \times 6 + 5^2$$

Correct answer: $$3 \times 5 + 6^2$$

Q4.

Using the formula $$x = 3a + t^2$$, if $$a = 3$$ and $$t = 1$$, what calculation would find $$x$$?

Correct answer: $$3^2 + 1$$

$$1^2 + 3$$

$$3^2 + 11$$

Q5.

Rearrange $$3m + t + 12 = 14g$$ to make $$t$$ the subject

Correct Answer: t = 14g - 3m - 12, t = 14g - 12 - 3m

Q6.

Rearrange $$3m - 5 = 14g - w$$ to make $$w$$ the subject

Correct Answer: w = 14g - 3m + 5, w = 14g + 5 - 3m

Exit quiz

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6 Questions

Q1.

What are the values of x that solve $$2x^2 + 12x + 10 = 0$$ ? (answer in the form "a,b")

Correct Answer: -5, -1, -1, -5

Q2.

What are the values of x that solve $$x^2 - 6x + 8 = 0$$ ? (answer in the form "a,b")

Correct Answer: 2,4, 4,2

Q3.

What are the values of x that solve $$3x^2 + 9x - 12 = 0$$ ? (answer in the form "a,b")

Correct Answer: -4,1, 1,-4

Q4.

What are the values of x that solve $$x^2 + 4x - 21 = 0$$ ? (answer in the form "a,b")

Correct Answer: -7,3, 3,-7

Q5.

What are the values of x that solve $$x^2 + 10x + 16 = 0$$ ? (answer in the form "a,b")

Correct Answer: -8,-2, -2,-8

Q6.

What are the values of x that solve $$ x^2 + 6x + 8 = 0$$ ? (answer in the form "a,b")

Correct Answer: -4,-2, -2,-4