Quadratic Function y=(x-4)²: Analyzing a 4-Unit Horizontal Shift

Question

y=(x−4)2 y=(x-4)^2 is the displacement function y=x2 y=x^2 right 4 steps

Video Solution

Solution Steps

00:00 Is this function the same as the function shifted 4 steps right?
00:06 Let's start by drawing the markings - we'll note the position 4 steps right
00:15 Let's draw the desired graph
00:19 Let's identify its intersection point with the X-axis
00:22 Let's substitute this point in the proposed function and check if it's correct
00:25 Let's substitute appropriate values and solve
00:28 The equation is correct, meaning the function is correct
00:32 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll verify if y=(x−4)2 y = (x-4)^2 is obtained by shifting y=x2 y = x^2 four units to the right:

  • Step 1: Identify transformation properties.
    The equation y=(x−h)2 y = (x-h)^2 indicates a horizontal shift of the parent function y=x2 y = x^2 .
  • Step 2: Determine the shift value from the expression.
    In y=(x−4)2 y = (x-4)^2 , h=4 h = 4 . This implies a shift 4 units to the right because h=4 h = 4 is positive.
  • Step 3: Verify the shift.
    If we replaced x x with x−4 x-4 , this represents taking the graph of y=x2 y = x^2 and shifting it rightwards by 4 units on the x-axis.

Therefore, we conclude that the function y=(x−4)2 y = (x-4)^2 does represent a displacement of y=x2 y = x^2 to the right by 4 units. Hence, the correct answer to the problem is True.

Answer

True

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Question Types

Parabola of the Form y=(x-p)²: True / false