Graph f(x)=x^2-4

Problem

ƒ(x)=x2−4

Solution

1. Identify the function type as a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=1 b=0 and c=−4

2. Determine the vertex by using the formula x=−b/(2*a) Since b=0 the vertex is at x=0 Substituting x=0 into the function gives ƒ(0)=−4 The vertex is (0,−4)

3. Find the y-intercept by evaluating ƒ(0) The y-intercept is (0,−4)

4. Find the x-intercepts by setting ƒ(x)=0 Solving x2−4=0 gives x2=4 so x=2 and x=−2 The x-intercepts are (2,0) and (−2,0)

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

6. Plot the points (0,−4) (2,0) and (−2,0) and draw a smooth U-shaped curve through them.

Final Answer

ƒ(x)=x2−4

The graph is a parabola opening upward with vertex at (0,−4) and x-intercepts at (−2,0) and (2,0)

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