Graph y=x^2+4x+4

Problem

y=x2+4*x+4

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2+b*x+c where a=1 b=4 and c=4 Since a>0 the parabola opens upward.

2. Factor the quadratic expression to find the xintercepts. The expression x2+4*x+4 is a perfect square trinomial.

(x+2)2=0

3. Determine the xintercept. Setting y=0 gives x=−2 Since there is only one solution, the vertex of the parabola touches the xaxis at (−2,0)

4. Find the yintercept by setting x=0

y=0+4*(0)+4

y=4

The yintercept is at (0,4)

5. Calculate the vertex using the formula x=(−b)/(2*a)

x=(−4)/(2*(1))

x=−2

Substituting x=−2 into the original equation gives y=0 The vertex is (−2,0)

6. Plot additional points to define the shape. For x=−1

y=(−1)2+4*(−1)+4

y=1

For x=−3

y=(−3)2+4*(−3)+4

y=1

7. Sketch the parabola passing through the points (−3,1) (−2,0) (−1,1) and (0,4)

Final Answer

y=(x+2)2

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