Solving quadratic equations by using the formula | Maths

Starter quiz

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

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

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

$\frac{20 \times 3 + 12 \times 3}{9}$
Using the formula $2m = 14x + y$ , if $x = 8$ and $y = 5$ , what calculation would find $m$ ?

$\frac{14 \times 8 + 5}{2}$ ✓

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

$\frac{14 \times 8 + 2}{5}$
Using the formula $x = 3a + t^2$ , if $a = 5$ and $t = 6$ , what calculation would find $x$ ?

$3 \times 5 + 2^6$

$3 \times 6 + 5^2$

$3 \times 5 + 6^2$ ✓
Using the formula $x = 3a + t^2$ , if $a = 3$ and $t = 1$ , what calculation would find $x$ ?

$3^2 + 1$ ✓

$1^2 + 3$

$3^2 + 11$
Rearrange $3m + t + 12 = 14g$ to make $t$ the subject

't = 14g - 3m - 12' ✓
Rearrange $3m - 5 = 14g - w$ to make $w$ the subject

'w = 14g - 3m + 5' ✓

Exit quiz

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

'-5, -1' ✓
What are the values of x that solve $x^2 - 6x + 8 = 0$ ? (answer in the form "a,b")

'2,4' ✓
What are the values of x that solve $3x^2 + 9x - 12 = 0$ ? (answer in the form "a,b")

'-4,1' ✓
What are the values of x that solve $x^2 + 4x - 21 = 0$ ? (answer in the form "a,b")

'-7,3' ✓
What are the values of x that solve $x^2 + 10x + 16 = 0$ ? (answer in the form "a,b")

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

'-4,-2' ✓

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Lesson Details

Key learning points

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