Vertex Representation: Transition between different representations of a function

Linking function properties to its representation
Question 1

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

Question 2

Find the standard representation of the following function

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

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

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

Question 5

Find the standard representation of the following function

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

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

Exercise #1

f(x)=(x−3)2+x f(x)=(x-3)^2+x

Video Solution

Answer

f(x)=x2−5x+9 f(x)=x^2-5x+9

Exercise #2

Find the standard representation of the following function

f(x)=(2x+1)2−1 f(x)=(2x+1)^2-1

Video Solution

Answer

f(x)=4x2+4x f(x)=4x^2+4x

Exercise #3

Find the standard representation of the following function

f(x)=(−x+1)2+3 f(x)=(-x+1)^2+3

Video Solution

Answer

f(x)=x2−2x+4 f(x)=x^2-2x+4

Exercise #4

Find the standard representation of the following function

f(x)=(x−2)2+3 f(x)=(x-2)^2+3

Video Solution

Answer

f(x)=x2−4x+7 f(x)=x^2-4x+7

Exercise #5

Find the standard representation of the following function

f(x)=(x+4)2−16 f(x)=(x+4)^2-16

Video Solution

Answer

f(x)=x2+8x f(x)=x^2+8x

Question 1

Find the standard representation of the following function

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

Question 2

Find the standard representation of the following function

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

Question 3

Find the standard representation of the following function

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

Question 4

Find the standard representation of the following function

\( f(x)=(-x-2)^2-5 \)

Question 5

Find the standard representation of the following function

\( f(x)=(x-6)^2+2x \)

Exercise #6

Find the standard representation of the following function

f(x)=(x−5)2−10 f(x)=(x-5)^2-10

Video Solution

Answer

f(x)=x2−10x+15 f(x)=x^2-10x+15

Exercise #7

Find the standard representation of the following function

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

Video Solution

Answer

f(x)=x2+10x+28 f(x)=x^2+10x+28

Exercise #8

Find the standard representation of the following function

f(x)=(x−2)2+4 f(x)=(x-2)^2+4

Video Solution

Answer

f(x)=x2−4x+8 f(x)=x^2-4x+8

Exercise #9

Find the standard representation of the following function

f(x)=(−x−2)2−5 f(x)=(-x-2)^2-5

Video Solution

Answer

f(x)=x2+4x−1 f(x)=x^2+4x-1

Exercise #10

Find the standard representation of the following function

f(x)=(x−6)2+2x f(x)=(x-6)^2+2x

Video Solution

Answer

f(x)=x2−10x+36 f(x)=x^2-10x+36