Interpreting parabola formulas

The general formula for a parabola is `ax^2+bx+c=y`

Positive and negative `x^2` coefficients

If `x^2` is positive then your parabola will look like this:

A positive parabola will look like this

If `x^2` is negative then your parabola will look like this:

A negative parabola will look like this

NOTE:

See later on finding the solution is finding the root or roots which is where the curve passes the `x` axis.

If in finding the solution to `ax^2+bx+c=y`

`x=+-sqrt(-12)` (for example)

It's not possible to find the square root of a negative number.

(To prove this put 3 then minus 6 into your calculator and then press the root button. You will get an error message.)

You are unable to find the root of a negative number

Your parabola will look something like the diagram below, meaning that the curve doesn't cross the `x` axis.

A negative parabola is not possible because it doesn’t go through the x axis

NOTE:

`x=+-sqrt(-12)` is called "Quadratics and complex numbers" and if you found this in an exam at this stage you've done something wrong.

If in finding the solution to:

`ax^2+bx+c=y`

`x=3` (for example)

And NOT `x=-1\ \ \ and\ \ \ 2`

Then your parabola will be turning on the `x` axis as follows:

A positive parabola will always touch or go through the x axis

`x=3` Would mean the parabola touches the `x` axis at `x=3` only, once.