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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 369 (page 977)

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

Short Answer

Expert verified

The solution in interval notation is $[- 3, 鈥� 4]$

Step by step solution

01

Step 1. Given information

$- x^{2} + x + 12 鈮� 0$

02

Step 2. Solve graphically

The quadratic equation is in standard form.

$- x^{2} + x + 12 鈮� 0$

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

The parabola opens downward.

Find the line of symmetry
$x = - \frac{b}{2 a} x = 0.5$

Find the vertex

$f (x) = - x^{2} + x + 12 f (0.5) = - {(0.5)}^{2} + (0.5) + 12 f (0.5) = 15$

vertex is $(0.5, 15)$

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

$f (x) = - x^{2} + x + 12 0 = - (x + 3) (x - 4) x = - 3 a n d x = 4$

The x-intercepts are $(- 3, 0) a n d (4, 0)$

The graph of the parabola is

03

Step 3. Solution

The solution in interval notation is $[- 3, 鈥� 4]$

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