Graph y=(x+1)^2

Problem

y=(x+1)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 (x+1) Since the constant is added to x inside the square, the graph shifts 1 unit to the left.

3. Locate the new vertex at (−1,0)

4. Find the yintercept by substituting x=0 into the equation, which gives y=(0+1)2=1 The yintercept is (0,1)

5. Calculate additional points to define the shape. For x=−2 y=(−2+1)2=1 For x=1 y=(1+1)2=4

6. Sketch the parabola passing through the points (−2,1) (−1,0) (0,1) and (1,4)

Final Answer

y=(x+1)2

Want more problems? Check here!