Parabola of the Form y=(x-p)²: Identify the positive and negative domain

Match functions to the appropriate graphsTrue / falseDetermine the algebraic representation of the following descriptionsFinding a stationary pointFinding Increasing or Decreasing Domains
Question 1

What is the positive domain of the function below?

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

Question 2

Find the positive area of the function

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

Question 3

Find the positive area of the function
\( y=(x+5)^2 \)

Question 4

Find the negative area of the function

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

Question 5

Find the negative area of the function

\( y+1=(x+3)^2 \)

Examples with solutions for Parabola of the Form y=(x-p)²: Identify the positive and negative domain

Exercise #1

What is the positive domain of the function below?

y=(x−2)2 y=(x-2)^2

Video Solution

Step-by-Step Solution

In the first step, we place 0 in place of Y:

0 = (x-2)²

 

We perform a square root:

0=x-2

x=2

And thus we reveal the point

(2, 0)

This is the vertex of the parabola.

 

Then we decompose the equation into standard form:

 

y=(x-2)²

y=x²-4x+2

Since the coefficient of x² is positive, we learn that the parabola is a minimum parabola (smiling).

If we plot the parabola, it seems that it is actually positive except for its vertex.

Therefore the domain of positivity is all X, except X≠2.

 

Answer

all x, x≠2 x\ne2

Exercise #2

Find the positive area of the function

y=(x+6)2 y=(x+6)^2

Video Solution

Answer

x≠−6 x\ne-6

Exercise #3

Find the positive area of the function
y=(x+5)2 y=(x+5)^2

Video Solution

Answer

For each X x≠5 x\ne5

Exercise #4

Find the negative area of the function

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

Video Solution

Answer

There is no

Exercise #5

Find the negative area of the function

y+1=(x+3)2 y+1=(x+3)^2

Video Solution

Answer

-4 < x < -2

Question 1

Find the positive area of the function

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

Question 2

Find the negative area of the function

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

Question 3

Find the negative area of the function

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

Question 4

Find the negative area of the function

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

Exercise #6

Find the positive area of the function

y=−(x−3)2 y=-(x-3)^2

Video Solution

Answer

There is no positive area.

Exercise #7

Find the negative area of the function

y=−(x+4)2 y=-(x+4)^2

Video Solution

Answer

For each X x≠−4 x\ne-4

Exercise #8

Find the negative area of the function

y−4=−(x−4)2 y-4=-(x-4)^2

Video Solution

Answer

x < 2 o x > 6

Exercise #9

Find the negative area of the function

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

Video Solution

Answer

-8 < x < -4