Graph y=x^2-1

Problem

y=x2−1

Solution

1. Identify the type of function. The equation y=x2−1 is a quadratic function in the form y=a*x2+b*x+c which represents a parabola.

2. Determine the vertex. Since b=0 the xcoordinate of the vertex is x=0 Substituting x=0 into the equation gives y=−1 The vertex is (0,−1)

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

y=0−1

y=−1

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

0=x2−1

x2=1

x=±1

5. Determine the opening direction. Since the coefficient of x2 is a=1 which is positive, the parabola opens upward.

6. Plot additional points to refine the shape. For x=2

y=2−1

y=3

For x=−2

y=(−2)2−1

y=3

Final Answer

y=x2−1

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