The shit blog of Paul Chris Jones

What does it mean to 'solve' a quadratic equation?
 Solving an equation means finding the value for x when y is a certain number, or vice versa.

Linear equations are easy to solve.
Here's an example:

y = 50x

What is the value of y when x = 2?

Ans: 

y = (50)(2) 

y = 100 when x = 2

What is the value of x when y = 10?

Ans: 

10 = 50x

10/50 = x

x = 1/5 when y = 10

Sometimes quadratic equations are more difficult to solve.
Let's look at an example:

y = x² + x

What's the value of y when x = 2?

Ans:

y = 2² + 2 = 4 + 2

y = 6 when x = 2

What's the value of x when y = 10?

Ans:

10 = x² + x

10 - x = x²

Then what?? 

It's impossible to find the answer by rearranging this equation.

You can see that finding the value of y with a given x value is easy, but when you need to do it the other way around it's a lot more difficult. There are 3 methods to find x values, which we'll go through in next few posts. They are:

1. The quadratic formula
2. Factorisation
3. Completing the square

Before we do that, there's a couple of things to tell you.
The first is, solving quadratics for values of y other than zero.
For example, you'll might get a question like this:

Solve this quadratic equation:
6= x² + x

All of the 3 methods for solving quadratic equations require that y = 0, however. So what do we do? We rearrange the equation so that one side is zero.

 6= x² + x
 0= x² + x -6

From this point we can start using one of the 3 methods for solving quadratics.


One more thing. With quadratic equations there will usually be 2 values for x for a given y value! But sometimes there'll only be 1... and sometimes none!
Look at the graphs below to see why:

When finding values of x for a known value of y, you will have to find 0, 1, or 2 values of x.