Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q

Solving quadratic equations by completing the square

Maths

Further algebraic terminology

Checking and securing understanding of factorising

Checking and securing understanding of forming linear equations

Checking and securing understanding of solving and interpreting linear equations

Checking and securing understanding of changing the subject

Checking and securing understanding of the product of two binomials

The product of three binomials

Factorising a quadratic expression

Factorising using the difference of two squares

Factorising quadratics of the form ax^2 + bx + c

Solving quadratic equations by factorising

Solving quadratic equations by factorising where rearrangement is required

Solving complex quadratic equations by completing the square

Solving quadratic equations by using the formula

Advanced problem solving with algebraic manipulation

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.

Algebraic manipulation

Write $$x^2 + 4x + 5$$ in the form of $$(x + p)^2 + q$$

Express $$x^2 + 6x + 10$$ as $$(x + p)^2 + q$$

Express $$x^2 + 8x + 14$$ as $$(x + p)^2 + q$$

Put $$x^2 - 4x + 5$$ in the form $$(x + p)^2 + q$$

Solve by completing the square: $$x^2 + 6x + 8 = 0$$

Solve by completing the square: $$x^2 + 6x + 5 = 0$$

Which of these is a solution for $$(x - 3)^2 = 0$$?

Which of these is a solution for $$x^2 = 0$$?

Which of these is a solution for $$(x - 4)(x + 2) = 0$$?

The equation for this curve is $$y=x^2 + 3x + 3$$. How many real solutions will it have? 

Rearrange the following equation to make $$m$$ the subject: $$3x - m = 9$$

Rearrange the following equation to make $$x$$ the subject: $$3x - m = 9$$

Solving quadratic equations by completing the square

Lesson outcome