### Home > A2C > Chapter 4 > Lesson 4.2.1 > Problem4-65

4-65.

Draw the graph of $y=2x^2+3x+1$. 2-82 HW eTool (Desmos). Homework Help ✎

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

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

$y=0+0+1$

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

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

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.

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

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

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

3. Find the coordinates of the vertex.

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

Use the eTool below to graph the equation.
Click the link at right for the full version of the eTool: CCA2 2-82 HW eTool