Draw the graph of $y=2x^2+3x+1$.

1. Find the $x$- and $y$-intercepts.

   Step 1 (a):

   To find the $y$-intercept, substitute $0$ for $x$.

   $y=0+0+1$

   Step 2 (a):

   To find the $x$-intercepts, factor the equation and substitute $0$ for $y$.

   $(2x+1)(x+1)=0$

   Answer (a):

   The $y$-intercept is $(0,1)$ and the $x$-intercepts are $(−1,0)$ and $\left(-\frac{1}{2}, 0 \right)$

2. Where is the line of symmetry of this parabola? Write its equation.

   Step (b):

   To find the line of symmetry, average the $x$-values of the
   $x$-intercepts.

   $x=\frac{-1-\frac{1}{2}}{2}$

   Answer (b):

   $x=-\frac{3}{4}$

3. Find the coordinates of the vertex.

   Step (c):

   Substitute the $x$-value for the line of symmetry into the equation.