Graph y=x^2+6x+5

Problem

y=x2+6*x+5

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 where a=1 b=6 and c=5 Since a>0 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 original equation to find the ycoordinate:

y=(−3)2+6*(−3)+5=9−18+5=−4

The vertex is (−3,−4)

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

y=(0)2+6*(0)+5=5

The yintercept is (0,5)

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

x2+6*x+5=0

(x+5)*(x+1)=0

x=−5,x=−1

The xintercepts are (−5,0) and (−1,0)

5. Plot the points and draw the curve. Use the vertex (−3,−4) the intercepts (0,5) (−5,0) and (−1,0) and the axis of symmetry x=−3 to sketch the parabola.

Final Answer

y=x2+6*x+5

The graph is an upward-opening parabola with vertex (−3,−4) yintercept (0,5) and xintercepts (−5,0) and (−1,0)

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