Graph y=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+c which represents a parabola.

2. Determine the vertex. Since there is no x term, the xcoordinate of the vertex is 0 Substituting x=0 into the equation gives y=−3 The vertex is (0,−3)

3. Find the yintercept. Setting x=0 results in y=−3 which is the vertex.

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

0=x2−3

x2=3

x=±√(,3)

5. Calculate 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, the points (−1,−2) and (−2,1) are also on the graph.

6. Plot the points (0,−3) (1,−2) (−1,−2) (2,1) and (−2,1) and connect them with a smooth U-shaped curve.

Final Answer

y=x2−3

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