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Year 10
Higher

Solving quadratic equations by using the formula

I can solve quadratic equations algebraically by using the formula.

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New
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Year 10
Higher

Solving quadratic equations by using the formula

I can solve quadratic equations algebraically by using the formula.

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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

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

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

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.


To help you plan your year 10 maths lesson on: Solving quadratic equations by using the formula, download all teaching resources for free and adapt to suit your pupils' needs...

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.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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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