Find the Positive Domain: Analyzing y=(x-2)² Function

What is the positive domain of the function below?

y=(x−2)2 y=(x-2)^2

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the positive domain of the function
00:03 Positive domain means above the X-axis
00:06 For this, we need to find the intersection points with the X-axis
00:09 At intersection points with X-axis, Y=0, we'll substitute and solve
00:13 Take the square root to eliminate the exponent
00:17 Isolate X
00:24 This is the intersection point with the X-axis
00:32 Use the shortened multiplication formulas and expand the brackets
00:36 Notice the coefficient of X squared is positive
00:39 When the coefficient is positive, the function is smiling
00:45 Draw the function based on intersection points and function type
00:55 The function is positive while it's above the X-axis
01:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the positive domain of the function below?

y=(x−2)2 y=(x-2)^2

2

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.

3

Final Answer

all x, x≠2 x\ne2

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

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

With the Y

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