Graph y=(x+5)^2

Problem

y=(x+5)2

Solution

1. Identify the parent function as y=x2 which is a parabola opening upward with its vertex at the origin (0,0)

2. Determine the horizontal shift by looking at the term inside the parentheses, (x+5)

3. Apply the transformation rule where y=(x−h)2 represents a shift of h units; here h=−5 so the graph shifts 5 units to the left.

4. Locate the new vertex at (−5,0)

5. Find the y-intercept by setting x=0 resulting in y=(0+5)2=25

6. Plot additional points such as (−4,1) and (−6,1) to define the width of the parabola.

7. Sketch the smooth U-shaped curve passing through these points, symmetric about the vertical line x=−5

Final Answer

y=(x+5)2

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