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

1. What are the $x$- and $y$-intercepts?

   Step 1 (a):

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

   Step 2 (a):

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

   Answer (a):

   The $y$-intercept is $(0,1)$ and the $x$-intercepts are $(−1,0)$ and

   $y=0+0+1$

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

   $\left(-\frac{1}{2}, 0 \right)$

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. What are the coordinates of the vertex?

   Step (c):

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