# Standard Representation - Examples, Exercises and Solutions

## Standard Form of the Quadratic Function

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

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

## Examples with solutions for Standard Representation

### Exercise #1

Find the standard representation of the following function

$f(x)=(x-2)(x+5)$

### Step-by-Step Solution

We will use the expanded distributive property.

(a+1)⋆(b+2) = ab+2a+b+2

Let's substitute the given values and solve:

(x-2)(x+5) =

x²-2x+5x+-2*5=

x²+3x-10

And that's the solution!

$f(x)+x^2+3x-10$

### Exercise #2

Create an algebraic expression based on the following parameters:

$a=2,b=2,c=2$

### Video Solution

$2x^2+2x+2$

### Exercise #3

Create an algebraic expression based on the following parameters:

$a=2,b=\frac{1}{2},c=4$

### Video Solution

$2x^2+\frac{1}{2}x+4$

### Exercise #4

Create an algebraic expression based on the following parameters:

$a=2,b=0,c=4$

### Video Solution

$2x^2+4$

### Exercise #5

Create an algebraic expression based on the following parameters:

$a=2,b=4,c=8$

### Video Solution

$2x^2+4x+8$

### Exercise #6

Create an algebraic expression based on the following parameters:

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

### Video Solution

$3x^2-3$

### Exercise #7

Choose the correct algebraic expression based on the parameters:

$a=-3,b=3,c=7$

### Video Solution

$-3x^2+3x+7$

### Exercise #8

Find the appropriate representation based on the parameters

$a=-3,b=4,c=-15$

### Video Solution

$-3x^2+4x-15$

### Exercise #9

Create an algebraic expression based on the following parameters:

$a=3,b=6,c=9$

### Video Solution

$3x^2+6x+9$

### Exercise #10

Create an algebraic expression based on the following parameters:

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

### Video Solution

$3x^2$

### Exercise #11

Create an algebraic expression based on the following parameters:

$a=4,b=-16,c=0$

### Video Solution

$4x^2-16x$

### Exercise #12

Create an algebraic expression based on the following parameters:

$a=4,b=-2,c=16$

### Video Solution

$4x^2-2x+16$

### Exercise #13

Create an algebraic expression based on the following parameters:

$a=4,b=2,c=5$

### Video Solution

$4x^2+2x+5$

### Exercise #14

Create an algebraic expression based on the following parameters:

$a=5,b=3,c=-4$

### Video Solution

$5x^2+3x-4$

### Exercise #15

Create an algebraic expression based on the following parameters:

$a=2,b=0,c=6$

### Video Solution

$2x^2+6$