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

4-65.
1. Draw the graph of y = 2x2 + 3x + 1. 4-65 HW eTool (Desmos). Homework Help ✎

1. Find the x- and y-intercepts.

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

3. Find the coordinates of the vertex.

Use the eTool below to graph the equation.
Click the link at right for the full version of the eTool: A2C 4-65 HW eTool

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

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

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

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

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

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