Graph y=(x+3)^2

Problem

y=(x+3)2

Solution

1. Identify the type of function. This is a quadratic function in vertex form y=a*(x−h)2+k where a=1 h=−3 and k=0

2. Determine the vertex. The vertex (h,k) is located at (−3,0)

3. Find the y-intercept. Set x=0 to find y=(0+3)2=9 The y-intercept is (0,9)

4. Identify the axis of symmetry. The vertical line passing through the vertex is x=−3

5. Plot additional points to define the shape. For x=−2 y=(−2+3)2=1 For x=−4 y=(−4+3)2=1

6. Sketch the parabola. Draw a smooth U-shaped curve opening upwards through the points (−3,0) (−2,1) (−4,1) and (0,9)

Final Answer

y=(x+3)2

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