Note that graph of a quadratic function is a parabola. To plot it, determine its vertex (h,k). To do so, apply the formula:
where a is the coefficient of x^2 and b coefficient of x.
In the function f(x)=x^2+8x+19, the values of a and b are 1 and 8, respectively. Plug-in these value to the formula to get h.
Then, evaluate the function f(x)=x^2+8x+19 when x=h to get the value of k.
Hence, the vertex of the parabola is (-4, 3).
Next, use additional two points to plot it. To do so, assign a value of x that is less than h. And solve for the corresponding value of y.
Also, assign a value of x that is greater than h.
So the other two points are (-6,7) and (-2,7).
Then, plot the vertex (-3,4) and the two points (-6,7) and (-2,7). Connect them and extend the parabola on both ends.
Hence, the graph of the given function is: