Graph f(x)=x^2-3

Problem

ƒ(x)=x2−3

Solution

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

2. Determine the vertex of the parabola. Since b=0 the xcoordinate of the vertex is x=0

3. Calculate the ycoordinate of the vertex by evaluating ƒ(0)=0−3=−3 The vertex is (0,−3)

4. Find the yintercept by setting x=0 which is (0,−3)

5. Find the xintercepts by setting ƒ(x)=0 resulting in x2−3=0 so x=±√(,3)≈±1.732

6. Plot additional points to determine the shape, such as ƒ(1)=−2 ƒ*(−1)=−2 ƒ(2)=1 and ƒ*(−2)=1

7. Sketch the graph as a parabola opening upward with its lowest point at (0,−3)

Final Answer

ƒ(x)=x2−3

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