Chapter 10: Q 340. (page 1240)

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.
$y = 2 x^{2} + 6 x + 2$

Short Answer

Expert verified

The required graph is shown below:

Step by step solution

Given information.

The given equation is $y = 2 x^{2} + 6 x + 2$

Determine the axis of symmetry.

By comparing the given equation with the standard form $y = a x^{2} + b x + c$ we get $a = 2, b = 6 a n d c = 2$

Since the value of a is positive so parabola opens up.

The axis of symmetry is the vertical line:

$x = - \frac{b}{2 a} = - \frac{6}{2 (2)} = - \frac{3}{2}$

The axis of symmetry is $x = - \frac{3}{2}$ .

Determine the vertex.

Put $x = - \frac{3}{2}$ into the given equation we get.

$y = 2 {(- \frac{3}{2})}^{2} + 6 (- \frac{3}{2}) + 2 = \frac{9}{2} - 9 + 2 = - \frac{5}{2}$

The vertex is $(- \frac{3}{2}, - \frac{5}{2})$ .

Determine the intercepts.

For y-intercept put $x = 0$ into the given equation.

$y = 2 {(0)}^{2} + 6 (0) + 2 = 2$

The y-intercept is $(0, 2)$ .

For x-intercept put $y = 0$ into the given equation.

$2 x^{2} + 6 x + 2 = 0 x = \frac{- 6 \pm \sqrt{6^{2} - 4 (2) (2)}}{2 (2)} = \frac{- 3 \pm \sqrt{5}}{2}$

The x-intercept is role="math" localid="1653824362529" $(\frac{- 3 + \sqrt{5}}{2}, 0) a n d (\frac{- 3 - \sqrt{5}}{2}, 0)$ .

Draw the graph.

By using the above information the required graph is shown below:

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Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.
$y = 2 x^{2} + 6 x + 2$

Short Answer

Step by step solution

Given information.

Determine the axis of symmetry.

Determine the vertex.

Determine the intercepts.

Draw the graph.

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Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.y=2x2+6x+2

Short Answer

Step by step solution

Given information.

Determine the axis of symmetry.

Determine the vertex.

Determine the intercepts.

Draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.
$y = 2 x^{2} + 6 x + 2$