Graph y-3=(x+2)^2

Problem

y−3=(x+2)2

Solution

1. Identify the form of the equation. The equation y−3=(x+2)2 is a parabola in vertex form, which is generally written as y−k=a*(x−h)2

2. Determine the vertex (h,k) By comparing y−3=(x+2)2 to the standard form, we find h=−2 and k=3 The vertex is (−2,3)

3. Identify the direction of opening. Since the coefficient a=1 is positive, the parabola opens upward.

4. Find the y-intercept by setting x=0

y−3=(0+2)2

y−3=4

y=7

The y-intercept is (0,7)

5. Find additional points using symmetry. Since the axis of symmetry is x=−2 the point symmetric to (0,7) is (−4,7)

6. Sketch the graph by plotting the vertex (−2,3) the y-intercept (0,7) and the symmetric point (−4,7) then drawing a smooth U-shaped curve through them.

Final Answer

y=(x+2)2+3

Want more problems? Check here!