Graph f(x)=x^2-9

Problem

ƒ(x)=x2−9

Solution

1. Identify the function type and its basic shape. The function ƒ(x)=x2−9 is a quadratic function in the form ƒ(x)=a*x2+b*x+c which represents a parabola opening upward because a=1

2. Determine the vertex of the parabola. Since there is no x term (b=0, the vertex lies on the yaxis at (0,c)

x=0

ƒ(0)=0−9=−9

The vertex is (0,−9)

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

x2−9=0

x2=9

x=±3

The xintercepts are (3,0) and (−3,0)

4. Find the y-intercept by evaluating the function at x=0

ƒ(0)=−9

The yintercept is (0,−9)

5. Plot additional points to refine the curve. For example, let x=1 and x=2

ƒ(1)=1−9=−8

ƒ(2)=2−9=−5

By symmetry, the points (−1,−8) and (−2,−5) are also on the graph.

6. Sketch the graph by drawing a smooth U-shaped curve through the points (−3,0) (−2,−5) (0,−9) (2,−5) and (3,0)

Final Answer

To graph ƒ(x)=x2−9 plot the vertex at (0,−9) the xintercepts at (−3,0) and (3,0) and draw an upward-opening parabola.

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