Vertical Shift: Find y = -(x-6)² + 4 After Translation

Question

Choose the equation that corresponds to the the function

y=−(x−6)2 y=-(x-6)^2

moved 4 spaces up.

Video Solution

Solution Steps

00:00 Express the new function
00:03 We will use the formula to shift the function
00:09 We want to shift 4 units horizontally upward, so we'll increase K
00:18 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the original function.
  • Step 2: Apply the vertical transformation.
  • Step 3: Confirm the new function equation matches a given choice.

Now, let's work through each step:
Step 1: The initial function is y=−(x−6)2 y = -(x-6)^2 . This represents a parabola that opens downward, vertex at (6,0).
Step 2: To shift the graph of the function 4 units up, we add 4 to the entire function:
y=−(x−6)2+4 y = -(x-6)^2 + 4 .
Step 3: Review the provided choices to find the match:
- Choice 4: y=−(x−6)2+4 y=-(x-6)^2+4 .
This matches our transformation result.

Therefore, the solution to the problem is y=−(x−6)2+4 y = -(x-6)^2 + 4 .

Answer

y=−(x−6)2+4 y=-(x-6)^2+4

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Related Subjects

Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts) Families of Parabolas

Question Types

Parabola of the Form y=(x-p)²+k: Determine the algebraic representation of the following descriptions