Graph f(x)=x^2-1

Problem

ƒ(x)=x2−1

Solution

1. Identify the type of function, which is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=1 b=0 and c=−1

2. Determine the shape of the graph, which is a parabola that opens upward because the leading coefficient a is positive.

3. Find the vertex of the parabola using the formula x=−b/(2*a)

x=−0/(2*(1))=0

4. Calculate the y-coordinate of the vertex by evaluating ƒ(0)

ƒ(0)=0−1=−1

5. Identify the vertex as the point (0,−1) which is also the y-intercept.

6. Find the x-intercepts by setting ƒ(x)=0 and solving for x

x2−1=0

x2=1

x=±1

7. Plot the key points (0,−1) (1,0) and (−1,0) and draw a smooth U-shaped curve through them.

Final Answer

ƒ(x)=x2−1

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