Graph x^2-1

Problem

y=x2−1

Solution

1. Identify the function type as a quadratic function in the form y=a*x2+b*x+c where a=1 b=0 and c=−1 This represents a parabola that opens upward because a>0

2. Find the vertex by using the formula x=−b/(2*a) Since b=0 the xcoordinate of the vertex is 0 Substituting x=0 into the equation gives y=−1 The vertex is (0,−1)

3. Determine the y-intercept by setting x=0

y=0−1

y=−1

The yintercept is (0,−1)

4. Find the x-intercepts by setting y=0 and solving for x

x2−1=0

x2=1

x=±1

The xintercepts are (1,0) and (−1,0)

5. Plot additional points to define the shape. For x=2

y=2−1

y=3

For x=−2

y=(−2)2−1

y=3

The points are (2,3) and (−2,3)

6. Sketch the graph by drawing a smooth U-shaped curve through the points (−2,3) (−1,0) (0,−1) (1,0) and (2,3)

Final Answer

y=x2−1

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