Standard Form of the Quadratic Function

The standard form of the quadratic function is:
$Y=ax^2+bx+c$

For example:
$Y=4x^2+3x+15$

Detailed explanation

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Test yourself on standard representation!

Create an algebraic expression based on the following parameters:

$$ a=3,b=0,c=-3 $$

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How do you go from standard form to vertex form?

We need to find the vertex of the parabola using the formula to find the $X$ vertex.
Let's find the $Y$ vertex.
Let's place in the vertex form template the $X$ vertex instead of $P$ , the $Y$ vertex instead of $C$ and the $a$ instead of $a$ .

How do you go from standard form to factored form?

Let's find the points of intersection of the parabola with the $x$ axis.
Let's place it in the factored form template.

Look!
If we were to realize that in the standard form there is a coefficient for $X^2$ we will place it in the factoring formula before locating the intersection points there, as follows:

$y=a\times(x-t)\times(x-k)$