Graph x^2-4

Problem

x2−4

Solution

1. Identify the type of function. The expression ƒ(x)=x2−4 is a quadratic function in the form ƒ(x)=a*x2+b*x+c which represents a parabola.

2. Determine the vertex. Since there is no x term (b=0, the xcoordinate of the vertex is x=0 Substituting x=0 into the function gives ƒ(0)=−4 The vertex is (0,−4)

3. Find the xintercepts by setting the expression equal to zero.

x2−4=0

(x−2)*(x+2)=0

x=2,x=−2

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

5. Plot the key points: the vertex at (0,−4) the xintercepts at (2,0) and (−2,0) and the yintercept at (0,−4) Draw a smooth U-shaped curve through these points.

Final Answer

y=x2−4

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