Determine the Intersection Points: Graphing y = (x-1)(x-1)

Determine the points of intersection of the function

y=(x1)(x1) y=(x-1)(x-1)

With the X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the intersection points with the X-axis
00:03 At the intersection points with the X-axis, the Y value must = 0
00:07 Substitute Y = 0 and solve to find X values
00:13 Find what makes each factor in the product zero
00:16 This is one solution
00:21 This solution makes both factors in the product zero
00:24 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Determine the points of intersection of the function

y=(x1)(x1) y=(x-1)(x-1)

With the X

2

Step-by-step solution

To solve this problem, we'll determine the intersection points of the function y=(x1)(x1) y = (x - 1)(x - 1) with the x-axis by following these steps:

  • Step 1: Set the function equal to zero to find where it intersects the x-axis.
  • Step 2: Solve the equation (x1)2=0(x - 1)^2 = 0.
  • Step 3: Determine the x-coordinate(s) from this equation.
  • Step 4: The y-coordinate will be zero at these points.

Let's work through these steps:

Step 1: We set the given function to zero: y=(x1)2=0 y = (x - 1)^2 = 0 .

Step 2: By solving the equation (x1)2=0(x - 1)^2 = 0, we apply the property that a square is zero only if the base is zero.

Step 3: Solving (x1)=0(x - 1) = 0, we find:

x=1 x = 1

Step 4: The corresponding point on the graph is (1,0)(1, 0), indicating where the function crosses the x-axis.

Therefore, the point of intersection of the function with the x-axis is (1,0) (1, 0) .

3

Final Answer

(1,0) (1,0)

Practice Quiz

Test your knowledge with interactive questions

The following function has been graphed below:

\( f(x)=-x^2+5x+6 \)

Calculate points A and B.

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