Graph y=(x+3)^2-4

Problem

y=(x+3)2−4

Solution

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

2. Determine the vertex by comparing the given equation to the vertex form. Here, h=−3 and k=−4

V=(−3,−4)

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

y=(0+3)2−4

y=9−4

y=5

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

0=(x+3)2−4

4=(x+3)2

±2=x+3

x=−1,x=−5

5. Determine the direction of the parabola. Since the coefficient a=1 is positive, the parabola opens upward.

6. Plot the points (−3,−4) (0,5) (−1,0) and (−5,0) on a coordinate plane and draw a smooth curve through them.

Final Answer

y=(x+3)2−4

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