Consider the function $y=x^2+5x+7$.

1. Complete the square to find the vertex.

   Hint (a):

   Add and subtract $\left ( \frac{5}{2} \right )^{2}$  on the same side of the equal sign.

   Step 1(a):

   $y=\left(x^2+5x+\left(\frac{5}{2}\right)^2\right)^2$

   Step 2(a):

   Simplify.

   $y=\left(x+2.5\right)^2+7-\frac{25}{4}$

   Step 3(a):

   Simplify more.

   $y=\left(x+2.5\right)^2+\frac{3}{4}$

2. Find the y-intercept.

   Hint (b):

   Substitute $0\ \text{for}\ x$ to find the y-intercept.

3. Use the vertex, the y-intercept, and the symmetry of parabolas to find a third point and sketch the graph.