Graph x^2-9

Problem

x2−9

Solution

1. Identify the type of function. The expression x2−9 is a quadratic function in the form ƒ(x)=a*x2+b*x+c which represents a parabola opening upwards since a=1

2. Find the y-intercept by setting x=0

ƒ(0)=0−9

ƒ(0)=−9

The y-intercept is at (0,−9)

3. Find the x-intercepts by setting the expression equal to zero and solving for x

x2−9=0

(x−3)*(x+3)=0

x=3,x=−3

The x-intercepts are at (3,0) and (−3,0)

4. Determine the vertex. Since there is no x term (b=0, the vertex lies on the y-axis.

(x_vertex)=−b/(2*a)=0

The vertex is (0,−9)

5. Sketch the graph by plotting the vertex (0,−9) and the intercepts (3,0) and (−3,0) then drawing a smooth U-shaped curve through these points.

Final Answer

y=x2−9

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