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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 364 (page 977)

In the following exercises, 鈸� solve graphically and 鈸� write the solution in interval notation
$x^{2} + 4 x - 12 < 0$

Short Answer

Expert verified

The solution in interval notation is $(- 6, 鈥� 2)$

Step by step solution

01

Step 1. Given information

$x^{2} + 4 x - 12 < 0$

02

Step 2. Solve graphically

The quadratic equation in standard form.

$x^{2} + 4 x - 12 < 0$

Graph the function $f (x) = x^{2} + 4 x - 12$

The parabola opens upward.

Find the line of symmetry

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

Find the vertex.

$f (x) = x^{2} + 4 x - 12 f (- 2) = - 16$

vertex $(- 2, - 16)$

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

$f (x) = x^{2} + 4 x - 12 0 = (x - 2) (x + 6) x = 2 a n d x = - 6$

The x-intercepts are $(2, 0)$ and $(- 6, 0)$

The graph of the parabola is

03

Step 3. Solution

The solution in interval notation is $(- 6, 2)$

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