Graph y=x^2-2x-8

Problem

y=x2−2*x−8

Solution

1. Identify the type of function and its orientation. The equation is a quadratic function in the form y=a*x2+b*x+c Since a=1 which is positive, 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 original equation to find the ycoordinate.

y=(1)2−2*(1)−8

y=−9

The vertex is (1,−9)

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

y=0−2*(0)−8

y=−8

The yintercept is (0,−8)

4. Find the x-intercepts by setting y=0 and factoring the quadratic.

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 a smooth curve. Use the vertex (1,−9) the yintercept (0,−8) and the xintercepts (−2,0) and (4,0) to sketch the parabola.

Final Answer

y=x2−2*x−8* is a parabola with vertex *(1,−9)* and intercepts *(−2,0),(4,0),(0,−8)

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