Standard form and parabolas are one of those things that you'll probably never use in life except while you're in school. I personally think you can get more information out of a vertex form rather than standard form. You are still required to know how to convert vertex form to standard form and vice versa to complete grade 10 mathematics in Ontario though.

A written post isn't always the best and least painful way to teach math, so here's a quick video that gets straight to the point. Afterwards, I'll break the steps down to pebbles and explain the method to this madness.

So first off, we'll use the formula mentioned in the video as a demonstration.

This is what vertex form looks like: y=a (x-h)2+k

And standard form looks like this: y=ax2+bx+c

The problem

Trying to get the vertex formed equation y=2(x+1)2-5 into standard form.

The solution

First, we must always follow the rule of BEDMAS. It says that we must factor the Brackets and Exponents first. Since x+1 is already in it's simplest form, we can't do anything to it. Now onto exponents. Since x+1 is squared, another way of writing (x+1)2 is (x+1)(x+1). We know this because whenever something is squared, something is being multiplied by itself. To clear things up a bit, let's see the formula looks like now:

y=2[(x+1)(x+1)]-5 Now the equation is in factored form.

Now, we move onto Multiplication. We can multiply 2 by (x+1). However, to make life more simple, always multiply the stuff in brackets first. In order to multiply this, we must use the rainbow rule, crabclaw or FOIL (or whatever you like to call it). Assuming that you know this (and you should by now), the result would be x2+2x+1. The formula now looks like:

y=2(x2+2x+1)+5

Now, we have to get rid of the brackets by multiplying 2 by everything inside the brackets.

y=2x2+4x+2+5

All you have to do now is simplify the formula by combining like terms. In this case the 2 and the 5 can be added to complete the problem. The final answer is....

y=2x2+4x+7