Graph y=(x+4)^2

Problem

y=(x+4)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+4) Since the constant 4 is added to x inside the square, the graph shifts 4 units to the left.

3. Locate the new vertex at (−4,0)

4. Find the y-intercept by substituting x=0 into the equation: y=(0+4)2=16 The y-intercept is (0,16)

5. Plot additional points to define the shape, such as x=−3 and x=−5 For both values, y=(−3+4)2=1=1 and y=(−5+4)2=(−1)2=1

6. Sketch the parabola passing through (−5,1) (−4,0) (−3,1) and (0,16)

Final Answer

y=(x+4)2

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