### Home > CCA2 > Chapter 2 > Lesson 2.2.1 > Problem2-82

2-82.

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

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

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.