Graph f(x)=x^2-2x-8

Problem

ƒ(x)=x2−2*x−8

Solution

1. Identify the function type and coefficients. This is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=1 b=−2 and c=−8 Since a>0 the parabola opens upward.

2. Find the vertex using the formula x=(−b)/(2*a)

x=(−(−2))/(2*(1))

x=1

Substitute x=1 into the function to find the ycoordinate.

ƒ(1)=(1)2−2*(1)−8

ƒ(1)=−9

The vertex is (1,−9)

3. Find the y-intercept by evaluating ƒ(0)

ƒ(0)=0−2*(0)−8

ƒ(0)=−8

The yintercept is (0,−8)

4. Find the x-intercepts by setting ƒ(x)=0 and factoring.

x2−2*x−8=0

(x−4)*(x+2)=0

x=4

x=−2

The xintercepts are (4,0) and (−2,0)

5. Plot the points and draw the smooth U-shaped curve (parabola) passing through (−2,0) (0,−8) (1,−9) and (4,0)

Final Answer

ƒ(x)=(x−1)2−9

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