Solve (x-5)² = 0: Finding X-Axis Intersections of a Quadratic Function

Find the intersection of the function

y=(x5)2 y=(x-5)^2

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 point of the function with the X-axis
00:03 At the intersection point with the X-axis Y=0
00:08 Therefore, substitute Y=0 and solve to find the intersection point with the X-axis
00:12 Extract the root to eliminate the exponent
00:24 Isolate X
00:31 This is the X value at the intersection point, we substitute Y=0 as we did at the point
00:36 And this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

Find the intersection of the function

y=(x5)2 y=(x-5)^2

With the X

2

Step-by-step solution

To find the intersection of the parabola y=(x5)2 y = (x-5)^2 with the x-axis, we must set the value of y y to zero since any point on the x-axis has a y-coordinate of zero.

Solving the equation:

  • Set (x5)2=0 (x-5)^2 = 0 .
  • To solve for x x , remove the square by taking the square root of both sides. This yields x5=0 x-5 = 0 .
  • Solve for x x by adding 5 to both sides: x=5 x = 5 .

Thus, the intersection point of the parabola with the x-axis is at (5,0) (5, 0) .

Therefore, the correct answer is (5,0) \boxed{(5,0)} , which corresponds to choice 3.

3

Final Answer

(5,0) (5,0)

Practice Quiz

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Find the intersection of the function

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

With the X

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