Graph f(x)=x^2+6x+8

Problem

ƒ(x)=x2+6*x+8

Solution

1. Identify the type of function and its orientation. This is a quadratic function in the form ƒ(x)=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=(−6)/(2*(1))=−3

Substitute x=−3 into the function to find the ycoordinate:

ƒ*(−3)=(−3)2+6*(−3)+8=9−18+8=−1

The vertex is (−3,−1)

3. Find the y-intercept by evaluating the function at x=0

ƒ(0)=0+6*(0)+8=8

The yintercept is (0,8)

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

x2+6*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 (−3,−1) the intercepts (−4,0) (−2,0) and (0,8) and the axis of symmetry x=−3 to sketch the parabola.

Final Answer

To graph ƒ(x)=x2+6*x+8 plot the vertex at (−3,−1) the xintercepts at (−4,0) and (−2,0) and the yintercept at (0,8)

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