Parabola of the Form y=(x-p)²+k: Finding Increasing or Decreasing Domains

Identify the positive and negative domainFinding a stationary pointDetermine the algebraic representation of the following descriptions
Question 1

Find the descending area of the function

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

Question 2

Find the descending area of the function

\( y=(x-4)^2-2x \)

Question 3

Find the ascending area of the function

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

Question 4

Find the ascending area of the function

\( y=(x+4)^2-5 \)

Question 5

Find the ascending area of the function

\( y=(x-6)^2+3 \)

Examples with solutions for Parabola of the Form y=(x-p)²+k: Finding Increasing or Decreasing Domains

Exercise #1

Find the descending area of the function

y=(x+2)2−1 y=(x+2)^2-1

Video Solution

Answer

x < -2

Exercise #2

Find the descending area of the function

y=(x−4)2−2x y=(x-4)^2-2x

Video Solution

Answer

x < 5

Exercise #3

Find the ascending area of the function

y=−(x+1)2+1 y=-(x+1)^2+1

Video Solution

Answer

x < -1

Exercise #4

Find the ascending area of the function

y=(x+4)2−5 y=(x+4)^2-5

Video Solution

Answer

-4 < x

Exercise #5

Find the ascending area of the function

y=(x−6)2+3 y=(x-6)^2+3

Video Solution

Answer

6 < x

Question 1

Find the descending area of the function

\( y=(x+1)^2+1 \)

Question 2

Find the descending area of the function

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

Question 3

Find the descending area of the function

\( y=(x+5)^2+5 \)

Question 4

Find the ascending area of the function

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

Question 5

Find the ascending area of the function

\( y=(x-6)^2+4 \)

Exercise #6

Find the descending area of the function

y=(x+1)2+1 y=(x+1)^2+1

Video Solution

Answer

x < -1

Exercise #7

Find the descending area of the function

y=−(x+2)2+4 y=-(x+2)^2+4

Video Solution

Answer

-2 < x

Exercise #8

Find the descending area of the function

y=(x+5)2+5 y=(x+5)^2+5

Video Solution

Answer

x < -5

Exercise #9

Find the ascending area of the function

y=−(x−2)2+1 y=-(x-2)^2+1

Video Solution

Answer

x < 2

Exercise #10

Find the ascending area of the function

y=(x−6)2+4 y=(x-6)^2+4

Video Solution

Answer

6 < x

Question 1

Find the descending area of the function

\( y=-(x+3)^2-10 \)

Exercise #11

Find the descending area of the function

y=−(x+3)2−10 y=-(x+3)^2-10

Video Solution

Answer

-3 < x