The document explains how to use the quadratic formula to find the roots or solutions of a quadratic equation. It provides the steps which are: 1) write the equation in standard form with all terms on one side, 2) identify the coefficients a, b, and c, and 3) substitute these coefficients into the quadratic formula. The formula is given as x = (-b ±√(b2 - 4ac))/2a. Worked examples are provided to demonstrate how to set up and solve a quadratic equation using the formula.

1. How to use the quadratic formula
to find roots of a quadratic
equation.

2. A
quadratic equation looks like this:
 ax² + bx + c = 0 (where ‘a’ cannot be zero.)
 Solving the equation means finding ‘x’ values
that make the equation true. These ‘x’ values
are called the roots of the quadratic.
 Quadratic equations can have 0, 1 or two
roots.

3. 



The general quadratic equation...
ax² + bx + c = 0
has roots
This formula, known as the ‘quadratic formula’, is
actually two formulas. The ‘±’ symbol should be
read as ‘plus or minus’, which means that you have
to work out the formula twice, once with a plus sign
in that position, then again with a minus sign. ...

4. STEPS
 Get
the equation in standar form (moving all
the terms to one side).
 Identify all the coeficients.
 Use the quadratic formula.

5. STEP 1
 Get
the equation in standar form (moving all
the terms to one side)
 Example
 2x² - 4x +1= 6+x²
 2x² - x²- 4x +1-6= 0
 x² - 4x - 5 = 0

6. STEP 2
Identify the coefficients ‘a’, ‘b’ and ‘c’ in your
quadratic equation, so that you can substitute them
into the formula to calculate ‘x’.
 For this equation:
x² - 4x - 5 = 0
There is no number written in front of the x² term, but
in that case it is helpful to think of the x² term as
1x² , so then:
a = 1, b = -4, and c = -5


7. STEP 3



Use the quadratic formula
Substitute the coefficients values into the formula.
In our example we get:
x² - 4x - 5 = 0
a = 1, b = -4, and c = -5
− (− 4) ± (− 4) 2 − 4 ⋅ 1 ⋅ (− 5)
x=
2 ⋅1
4 ± 36
2
Calculating the square root, we have two solutions:
x=
4+ 6
x=
=5
2
x=
4−6
= −1
2

8. YOUR TURN !
 21x2
+ 100 = - 5
 x2 - 3x + 2 = 0
 2x2 - 6x = 6x2 - 8x
 14x2 - 28 = 0
 x2 = 7x
 (x - 3)2 - (2x + 5)2 = - 16

9. SOLUTIONS
{
0,5}
 { 1,2}
 { 0, 0.5 }
{
}
{ 0 , 7 }
{
}

10. SOLUTIONS
{
0,5}
 { 1,2}
 { 0, 0.5 }
{
}
{ 0 , 7 }
{
}