Graph x^2-3

Problem

y=x2−3

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=0 and c=−3 The graph is a parabola that opens upward because a>0

2. Determine the vertex. Since b=0 the xcoordinate of the vertex is x=0 Substituting x=0 into the equation gives y=−3 The vertex is (0,−3)

3. Find the yintercept. Set x=0 to find the point where the graph crosses the yaxis.

y=0−3

y=−3

The yintercept is (0,−3)

4. Find the xintercepts. Set y=0 and solve for x

x2−3=0

x2=3

x=±√(,3)

The xintercepts are approximately (1.73,0) and (−1.73,0)

5. Plot additional points to define the shape. For x=1 y=1−3=−2 For x=2 y=2−3=1 Due to symmetry across the yaxis (x=0, the points (−1,−2) and (−2,1) are also on the graph.

6. Sketch the curve. Draw a smooth, U-shaped curve passing through the vertex (0,−3) and the calculated points.

Final Answer

y=x2−3

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