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

Problem

y=(x+2)2−3

Solution

1. Identify the form of the equation. This is a quadratic function in vertex form, y=a*(x−h)2+k

2. Determine the vertex (h,k) by comparing the given equation to the vertex form. Here, h=−2 and k=−3

V=(−2,−3)

3. Find the y-intercept by setting x=0 and solving for y

y=(0+2)2−3

y=4−3=1

y-intercept=(0,1)

4. Find the x-intercepts by setting y=0 and solving for x

0=(x+2)2−3

(x+2)2=3

x+2=±√(,3)

x=−2±√(,3)

x-intercepts≈(−0.27,0),(−3.73,0)

5. Identify the axis of symmetry, which is the vertical line passing through the vertex.

x=−2

6. Determine the direction of opening by looking at the coefficient a Since a=1 which is positive, the parabola opens upward.

Final Answer

To graph the function y=(x+2)2−3 plot the vertex at (−2,−3) the y-intercept at (0,1) and the x-intercepts at approximately (−0.27,0) and (−3.73,0) then draw a smooth upward-opening parabola through these points.

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