Graph f(x)=x^2-7

Problem

ƒ(x)=x2−7

Solution

1. Identify the type of function. This is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=1 b=0 and c=−7 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=0 Substituting this into the function gives ƒ(0)=−7 The vertex is (0,−7)

3. Find the yintercept. Set x=0 to find the yintercept, which is (0,−7) This point also serves as the vertex.

4. Find the xintercepts. Set ƒ(x)=0 and solve for x

x2−7=0

x2=7

x=±√(,7)

The xintercepts are approximately (−2.65,0) and (2.65,0)

5. Plot additional points to define the shape. For x=1 ƒ(1)=1−7=−6 For x=2 ƒ(2)=2−7=−3 For x=3 ƒ(3)=3−7=2 Use symmetry across the yaxis to find the corresponding points (−1,−6) (−2,−3) and (−3,2)

6. Sketch the curve. Draw a smooth, U-shaped curve passing through the vertex (0,−7) and the calculated points.

Final Answer

ƒ(x)=x2−7

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