# Standard Form of the Quadratic Function

🏆Practice standard representation

## Standard Form of the Quadratic Function

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

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

## Test yourself on standard representation!

Create an algebraic expression based on the following parameters:

$$a=-1,b=-1,c=-1$$

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:

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

## Examples and exercises with solutions of the Standard form of the quadratic function

### Exercise #1

Create an algebraic expression based on the following parameters:

$a=-1,b=-1,c=-1$

### Video Solution

$-x^2-x-1$

### Exercise #2

Create an algebraic expression based on the following parameters:

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

### Video Solution

$3x^2-3$

### Exercise #3

Create an algebraic expression based on the following parameters:

$a=1,b=-1,c=1$

### Video Solution

$x^2-x+1$

### Exercise #4

Create an algebraic expression based on the following parameters:

$a=-1,b=-8,c=0$

### Video Solution

$-x^2-8x$

### Exercise #5

Create an algebraic expression based on the following parameters:

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

### Video Solution

$3x^2$