Graph f(x)=x^2-10

Problem

ƒ(x)=x2−10

Solution

1. Identify the type of function, which is a quadratic function in the form ƒ(x)=a*x2+b*x+c

2. Determine the vertex of the parabola. Since b=0 the xcoordinate of the vertex is x=0

3. Calculate the ycoordinate of the vertex by evaluating ƒ(0)=0−10=−10 The vertex is (0,−10)

4. Find the yintercept by setting x=0 which is (0,−10)

5. Find the xintercepts by setting ƒ(x)=0 resulting in x2=10 so x=±√(,10)≈±3.16

6. Plot additional points to determine the width, such as ƒ(2)=2−10=−6 and ƒ*(−2)=(−2)2−10=−6

7. Sketch the upward-opening parabola passing through these points.

Final Answer

ƒ(x)=x2−10

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