Graph f(x)=(x+2)^2-1

Problem

ƒ(x)=(x+2)2−1

Solution

1. Identify the form of the function. The equation is in vertex form, ƒ(x)=a*(x−h)2+k where (h,k) is the vertex.

2. Determine the vertex by identifying h and k Since the expression is (x+2)2−1 we have h=−2 and k=−1

3. Find the vertex coordinates.

V=(−2,−1)

4. Determine the axis of symmetry, which is the vertical line passing through the vertex.

x=−2

5. Find the y-intercept by evaluating the function at x=0

ƒ(0)=(0+2)2−1=4−1=3

6. Find the x-intercepts by setting ƒ(x)=0 and solving for x

(x+2)2−1=0

(x+2)2=1

x+2=±1

x=−1,x=−3

7. Plot the points and draw the parabola. The parabola opens upward because the leading coefficient a=1 is positive.

Final Answer

ƒ(x)=(x+2)2−1* is a parabola with vertex *(−2,−1)* and y-intercept *(0,3)

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