Graph x^2+2x+1

Problem

x2+2*x+1

Solution

1. Identify the type of function. The expression x2+2*x+1 is a quadratic function in the form a*x2+b*x+c where a=1 b=2 and c=1 Since a>0 the parabola opens upward.

2. Factor the expression to find the roots. The expression is a perfect square trinomial.

(x+1)2=0

3. Determine the x-intercept. Setting the factored form to zero gives x=−1 This means the parabola touches the x-axis at the point (−1,0)

4. Find the vertex. For a perfect square (x−h)2+k the vertex is (h,k) Here, x2+2*x+1=(x+1)2+0 so the vertex is (−1,0)

5. Calculate the y-intercept. Set x=0 in the original equation.

0+2*(0)+1=1

The y-intercept is at (0,1)

6. Plot additional points to define the curve. Using symmetry around the axis of symmetry x=−1 if (0,1) is on the graph, then (−2,1) must also be on the graph.

Final Answer

x2+2*x+1=(x+1)2

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