Pre-Calc 11: Week 9 – General Form and Standard Form

This week we learned how to convert from General to Standard form.

Both of these forms tell you something about the parabola / equation you are dealing with.

General Form:

$y = ax^2 + bx + c$

C is the y-intercept

A will tell you the scale factor and if it opens up or down

This formula is nice but you will learn more from standard form.

In order to get to standard form you will have to complete the square.

So if your general form looks like: $y = 2x^2 + 8x -5$

You will first have to take “a” out of the first two terms:

$y = 2(x^2 + 4x) -5$

Then complete the square:

$y = 2(x^2 +4x +4 -4) -5$

Before you can take the extra -4 out of the perfect square trinomial to group it with -5, you must multiply it by the 2 out in front:

$y = 2(x+2)^2 -8 -5$

$y = 2(x+2)^2 -13$

Your equation is now in standard form.

This is also represented as $y = a(x+p)^2 - q$

A tells you the scale factor and if the parabola opens up or down.

P and Q tell you your vertex.

It also tells you your maximum/minumum, your axis of symmetry and your domain and range.