Graph y=x^2+4x+3

Problem

y=x2+4*x+3

Solution

1. Identify the type of function by observing that the equation is in the standard quadratic form y=a*x2+b*x+c where a=1 b=4 and c=3 Since a>0 the parabola opens upward.

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

x=−4/(2*(1))

x=−2

3. Find the y-coordinate of the vertex by substituting x=−2 back into the original equation.

y=(−2)2+4*(−2)+3

y=4−8+3

y=−1

The vertex is at (−2,−1)

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

y=(0)2+4*(0)+3

y=3

The y-intercept is (0,3)

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

0=x2+4*x+3

0=(x+3)*(x+1)

x=−3,x=−1

The x-intercepts are (−3,0) and (−1,0)

6. Plot the points and draw a smooth curve through the vertex (−2,−1) the x-intercepts (−3,0) and (−1,0) and the y-intercept (0,3)

Final Answer

y=x2+4*x+3

The graph is a parabola opening upward with vertex (−2,−1) x-intercepts at x=−3 and x=−1 and y-intercept at y=3

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