Standard Representation: Transition between different representations of a function

Determine the algebraic representation of the following descriptions

Question 1

Find the standard representation of the following function

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

Question 2

Find the standard representation of the following function

$$ f(x)=3x(x+4) $$

Question 3

Find the standard representation of the following function

$$ f(x)=(x+2)(x-4) $$

Question 4

Find the standard representation of the following function

$$ f(x)=(x-6)(x-2) $$

Question 5

Find the standard representation of the following function

$$ f(x)=-x(x-8) $$

Examples with solutions for Standard Representation: Transition between different representations of a function

Exercise #1

Find the standard representation of the following function

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

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

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

Exercise #2

Find the standard representation of the following function

$f(x)=3x(x+4)$

Video Solution

Answer

$f(x)=3x^2+12x$

Exercise #3

Find the standard representation of the following function

$f(x)=(x+2)(x-4)$

Video Solution

Answer

$f(x)=x^2-2x-8$

Exercise #4

Find the standard representation of the following function

$f(x)=(x-6)(x-2)$

Video Solution

Answer

$f(x)=x^2-8x+12$

Exercise #5

Find the standard representation of the following function

$f(x)=-x(x-8)$

Video Solution

Answer

$f(x)=-x^2+8x$

Question 1

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

Question 2

Find the representation of the product of the following function

$$ f(x)=x^2-2x-3 $$

Question 3

Find the representation of the product of the following function

$$ f(x)=x^2-3x-18 $$

Question 4

Find the representation of the product of the following function

$$ f(x)=x^2-7x+12 $$

Question 5

Find the representation of the product of the following function

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

Exercise #6

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

Video Solution

Answer

$f(x)=x^2-5x+9$

Exercise #7

Find the representation of the product of the following function

$f(x)=x^2-2x-3$

Video Solution

Answer

$(x-3)(x+1)$

Exercise #8

Find the representation of the product of the following function

$f(x)=x^2-3x-18$

Video Solution

Answer

$(x-6)(x+3)$

Exercise #9

Find the representation of the product of the following function

$f(x)=x^2-7x+12$

Video Solution

Answer

$(x-3)(x-4)$

Exercise #10

Find the representation of the product of the following function

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

Video Solution

Answer

$(x+2)(x-1)$

Question 1

Find the standard representation of the following function

$$ f(x)=(2x+1)^2-1 $$

Question 2

Find the standard representation of the following function

$$ f(x)=(2x+1)(x-2) $$

Question 3

Find the standard representation of the following function

$$ f(x)=(-x+1)^2+3 $$

Question 4

Find the standard representation of the following function

$$ f(x)=(x+1)(x-1) $$

Question 5

Find the standard representation of the following function

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

Exercise #11

Find the standard representation of the following function

$f(x)=(2x+1)^2-1$

Video Solution

Answer

$f(x)=4x^2+4x$

Exercise #12

Find the standard representation of the following function

$f(x)=(2x+1)(x-2)$

Video Solution

Answer

$f(x)=2x^2-3x-2$

Exercise #13

Find the standard representation of the following function

$f(x)=(-x+1)^2+3$

Video Solution

Answer

$f(x)=x^2-2x+4$

Exercise #14

Find the standard representation of the following function

$f(x)=(x+1)(x-1)$

Video Solution

Answer

$f(x)=x^2-1$

Exercise #15

Find the standard representation of the following function

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

Video Solution

Answer

$f(x)=x^2-4x+7$

Question 1

Find the standard representation of the following function

$$ f(x)=(x+3)(-x-4) $$

Question 2

Find the standard representation of the following function

$$ f(x)=(x+4)^2-16 $$

Question 3

Find the standard representation of the following function

$$ f(x)=(x-5)^2-10 $$

Question 4

Find the standard representation of the following function

$$ f(x)=(x+5)^2+3 $$

Question 5

Find the representation of the product of the following function

$$ f(x)=x^2+12x+32 $$

Exercise #16

Find the standard representation of the following function

$f(x)=(x+3)(-x-4)$

Video Solution

Answer

$f(x)=-x^2-7x-12$

Exercise #17

Find the standard representation of the following function

$f(x)=(x+4)^2-16$

Video Solution

Answer

$f(x)=x^2+8x$

Exercise #18

Find the standard representation of the following function

$f(x)=(x-5)^2-10$

Video Solution

Answer

$f(x)=x^2-10x+15$

Exercise #19

Find the standard representation of the following function

$f(x)=(x+5)^2+3$

Video Solution

Answer

$f(x)=x^2+10x+28$

Exercise #20

Find the representation of the product of the following function

$f(x)=x^2+12x+32$

Video Solution

Answer

$(x+8)(x+4)$