How to solve quadratics

the different ways to solve them!

HideShow resource information
  • Created by: Kelly:)
  • Created on: 03-06-11 20:29

Factorising

1. factorise!
find two numbers that will fit in the two brackets to help you solve the formula. They need to add to give the coefficient of 'x' and mulitply to give the number itself at the end of the equation. These two numbers must fit in with both parts.

Use FOIL to find out if it's right:
First
Outer
Inner
Last

When you have your two brackets, they both must equal zero to solve the equation, eg.,
(x + 5)(x - 2) = 0
so x = -5/2

1 of 4

Completing the Square

2. This looks like (x + p)^2 + q.

You need to halve the coefficient of x from the equation given.
You need to minus the amount created from the bracket and add/minus the value from the equation given.
You need to tidy it up by making this just one number.

Eg.,
x^2 + 4x - 5
becomes...
(x + 2)^2 - 4 - 5
tidier..
(x + 2)^2 - 9

2 of 4

The Quadratic Equation

3. If nothing else works: use the equation!

x = (-b +/- ((square root) b^2 - 4ac)) / 2a

equation given: x^2 + 6x + 10
a = 1
b = 6
c = 10

if your 'b' value is already a minus then it becomes positive.

This will only be on a calculator paper.

3 of 4

Graphing

4. You may need to solve them using graphs.

Look at the 'x' values on the graph paper given to find out what values you should work out the equation for.

Write these in a table, the values will usually be from -3 to 3 or something similar.

Where the graph crosses the x-axis will be the values to your equation. A straight line graph will only give you one value, however you may be asked to draw a quadratic graph and a straight line, the points where these two cross gives you your values.

An x^2 graph = dip
An x^3 graph = 'S'

4 of 4

Comments

Joe Mount

Kelly :) isn't the quadratic equation one where its just x^2 1? rather than zero? cause you can have 0x?

Kelly:)

oh yeah :) that's what i meant :P

Similar Mathematics resources:

See all Mathematics resources »See all Quadratic equations resources »