Graph y=x^2+6x+8

Problem

y=x2+6*x+8

Solution

1. Identify the type of function and its orientation. This 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 x-intercepts by setting y=0 and factoring the quadratic expression.

x2+6*x+8=0

(x+2)*(x+4)=0

x=−2,x=−4

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

y=0+6*(0)+8

y=8

4. Calculate the vertex using the formula x=(−b)/(2*a) for the x-coordinate.

x=(−6)/(2*(1))=−3

Substitute x=−3 into the original equation to find the y-coordinate.

y=(−3)2+6*(−3)+8

y=9−18+8=−1

The vertex is at (−3,−1)

5. Determine the axis of symmetry, which is the vertical line passing through the vertex.

x=−3

6. Plot the key points (vertex, intercepts, and their reflections) and draw a smooth U-shaped curve.

Final Answer

y=x2+6*x+8

Want more problems? Check here!