The graph of a quadratic equation can show if there are solutions when the equation is equal to zero.
A quadratic might be the product of two binomial expressions.
If you find the two binomial expressions then you can find the values for x
The product is equal to zero, meaning that one of the two binomial expressions must equal zero.
You can set each expression to zero to find the value for x

Keywords

Factorise - To factorise is to express a term as the product of its factors.
Solution (equality) - A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.
Parabola - A parabola is a curve where any point on the curve is an equal distance from: a fixed point (the focus ), and a fixed straight line (the directrix ).

Common misconception

That the solutions are just the constants in the binomials.

After factorising, pupils should be writing the one step equations, equal to zero, before writing the solutions.

Pupils can use graphing software to check their solutions. This will reinforce the reason why the binomials can be put equal to zero to solve, and help with features of quadratic graphs when they explore this further.

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.

Factorise the expression: $$x^2 - 9x + 14$$

Correct Answer: (x - 2)(x - 7), (x - 7)(x - 2)

Q2.

Factorise the expression: $$x^2 - 6x + 9$$

Correct answer: $$(x - 3)^2$$

$$(x + 3)^2$$

$$(x - 9)(x + 1)$$

Q3.

Factorise the expression: $$16x^2 - 9$$

Correct Answer: (4x - 3)(4x + 3), (4x + 3)(4x - 3)

Q4.

Factorise the expression: $$25y^2 - 64$$

Correct Answer: (5y - 8)(5y + 8), (5y + 8)(5y - 8)

Q5.

Factorise the expression: $$4x^2 - 4x - 15$$

Correct Answer: (2x - 5)(2x + 3), (2x + 3)(2x - 5)

Q6.

Factorise the expression: $$3x^2 + 12x + 12$$

Correct answer: $$3(x + 2)^2$$

$$3(x + 4)(x + 3)$$

$$(x + 4)^2$$

Exit quiz

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6 Questions

Q1.

Solve: $$(x-4)(x+2)=0$$

Correct answer: $$x = 4, x = -2$$

$$ x = 4, x = 2$$

$$ x = -4, x = -2$$

Q2.

Solve: $$x^2 - 5x + 6 = 0$$

$$x = 1, x = 6$$

Correct answer: $$ x = 2, x = 3$$

$$ x = 3, x = -2$$

Q3.

Solve: $$2x^2 - 8x = 0$$

Correct answer: $$x = 0, x = 4$$

$$x = 0, x = -4$$

$$x = 4, x = -4$$

Q4.

Solve: $$x^2 + x - 12 = 0$$

$$x = 2, x = 6$$

Correct answer: $$x = 3,x = -4$$

$$x = 4, x = -3$$

Q5.

Solve: $$(2x-6)(x-9)=0$$

$$x = 3, x = -9$$

Correct answer: $$x = 3, x = 9$$

$$x =-3,x = 9$$

Q6.

Solve: $$x^2 - 9x + 20 = 0$$

$$x = 3 , x = 7$$

$$x = 1, x = 20$$

Correct answer: $$x = 4, x = 5$$