Standard Form of the Quadratic Function

The standard form of the quadratic function is:
Y=ax2+bx+cY=ax^2+bx+c

For example:
Y=4x2+3x+15Y=4x^2+3x+15

Practice Standard Representation

Examples with solutions for Standard Representation

Exercise #1

Find the standard representation of the following function

f(x)=(x2)(x+5) f(x)=(x-2)(x+5)

Video Solution

Step-by-Step Solution

We will begin by using the distributive property in order to expand the following expression.

(a+1)⋆(b+2) = ab+2a+b+2

We will then proceed to insert the known values into the equation and solve as follows:

(x-2)(x+5) =

x²-2x+5x+-2*5=

x²+3x-10

And that's the solution!

Answer

f(x)+x2+3x10 f(x)+x^2+3x-10

Exercise #2

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

x2x1 -x^2-x-1

Exercise #3

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

3x23 3x^2-3

Exercise #4

Create an algebraic expression based on the following parameters:


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

Video Solution

Answer

x2x+1 x^2-x+1

Exercise #5

Create an algebraic expression based on the following parameters:


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

Video Solution

Answer

x28x -x^2-8x

Exercise #6

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

3x2 3x^2

Exercise #7

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

2x2+4x+8 2x^2+4x+8

Exercise #8

Create an algebraic expression based on the following parameters:

a=2,b=12,c=4 a=2,b=\frac{1}{2},c=4

Video Solution

Answer

2x2+12x+4 2x^2+\frac{1}{2}x+4

Exercise #9

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

4x216x 4x^2-16x

Exercise #10

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

x2+x -x^2+x

Exercise #11

Create an algebraic expression based on the following parameters:

a=0,b=1,c=0 a=0,b=1,c=0

Video Solution

Answer

x x

Exercise #12

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

x2 -x^2

Exercise #13

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

3x2+6x+9 3x^2+6x+9

Exercise #14

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

2x2+6 2x^2+6

Exercise #15

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

2x2+4 2x^2+4