Graph f(x)=x^2-8

Problem

ƒ(x)=x2−8

Solution

1. Identify the type of function. This 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 vertex is located on the yaxis at (0,−8)

3. Find the xintercepts by setting ƒ(x)=0

x2−8=0

x2=8

x=±√(,8)

x≈±2.83

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

5. Plot additional points to refine the shape. For example, if x=2 ƒ(2)=2−8=−4 If x=−2 ƒ*(−2)=(−2)2−8=−4

6. Sketch the curve through the vertex (0,−8) the xintercepts (±2.83,0) and the points (±2,−4)

Final Answer

ƒ(x)=x2−8

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