Graph y=x^2-8

Problem

y=x2−8

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=−8 The graph is a parabola that opens upward because a>0

2. Determine the vertex. Since b=0 the xcoordinate of the vertex is x=−b/(2*a)=0 Substituting x=0 into the equation gives y=0−8=−8 The vertex is (0,−8)

3. Find the yintercept. Set x=0 to find the point where the graph crosses the yaxis.

y=0−8=−8

The yintercept is (0,−8)

4. Find the xintercepts. Set y=0 and solve for x

0=x2−8

x2=8

x=±√(,8)=±2√(,2)≈±2.83

The xintercepts are (2√(,2),0) and (−2√(,2),0)

5. Plot additional points to define the shape.
   If x=1 y=1−8=−7 Point: (1,−7)
   If x=−1 y=(−1)2−8=−7 Point: (−1,−7)
   If x=3 y=3−8=1 Point: (3,1)
   If x=−3 y=(−3)2−8=1 Point: (−3,1)

6. Sketch the curve. Draw a smooth U-shaped curve (parabola) passing through the vertex (0,−8) the xintercepts, and the additional points.

Final Answer

The graph of y=x2−8 is a parabola with vertex (0,−8) yintercept (0,−8) and xintercepts (±2√(,2),0)

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