Graph y=x^2-9

Problem

y=x2−9

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2+b*x+c where a=1 b=0 and c=−9 The graph is a parabola that opens upward because a>0

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

y=0−9

y=−9

The y-intercept is (0,−9)

3. Find the x-intercepts by setting y=0 and solving for x

x2−9=0

x2=9

x=±3

The x-intercepts are (3,0) and (−3,0)

4. Determine the vertex. Since b=0 the x-coordinate of the vertex is x=(−b)/(2*a)=0 Substituting x=0 into the equation gives y=−9 The vertex is (0,−9)

5. Plot the points (0,−9) (3,0) and (−3,0) on a coordinate plane and draw a smooth U-shaped curve passing through them.

Final Answer

y=x2−9

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