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

Solving quadratic equations by using the formula

Maths

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.

Algebraic manipulation

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

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

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

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

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

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

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

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

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

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

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

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

This lesson will be removed by end of Summer Term 2025.

Solving quadratic equations by using the formula

Lesson outcome

This lesson will be removed by end of Summer Term 2025.