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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q 365 (page 977)

In the following exercises, 鈸� solve graphically and 鈸� write the solution in interval notation
$x^{2} + 4 x + 3 鈮� 0$

Short Answer

Expert verified

The solution in interval notation is $鈥� [- 3, 鈥� - 1]$

Step by step solution

01

Step 1. Given information

$x^{2} + 4 x + 3 鈮� 0$

02

Step 2. Solve graphically

The quadratic equation in standard form.

$x^{2} + 4 x + 3 鈮� 0$

Graph the function $f (x) = x^{2} + 4 x + 3$

The parabola opens upward.

Find the line of symmetry

$x = - \frac{b}{2 a} x = - 2$

Find the vertex.

$f (x) = x^{2} + 4 x + 3 f (- 2) = - 1$

vertex $(- 2, - 1)$

Find the x-intercepts. Let $f (x) = 0$

$f (x) = x^{2} + 4 x + 3 0 = (x + 1) (x + 3) x = - 1 a n d x = - 3$

The x-intercepts are $(- 1, 0) a n d (- 3, 0)$

03

Step 3. Solution

The solution in interval notation is $[- 3, 鈥� - 1]$

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