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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q 368 (page 1069)

In the following exercises, 鈸� solve graphically and 鈸� write the solution in interval notation $- x^{2} + 2 x + 24 < 0$

Short Answer

Expert verified

The solution in interval notation is $(- 鈭� 鈥�, 鈥� - 4) 鈭� (6, 鈥� 鈭� 鈥�)$

Step by step solution

01

Step 1. Given information

$- x^{2} + 2 x + 24 < 0$

02

Step 2. Solve graphically

The quadratic equation is in standard form.

$- x^{2} + 2 x + 24 < 0$

Graph the function $f (x) = - x^{2} + 2 x + 24$

The parabola opens downward.

Find the line of symmetry

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

Find the vertex

$f (x) = - x^{2} + 2 x + 24 f (1) = - {(1)}^{2} + 2 (1) + 24 f (1) = 25$

vertex is $(1, 25)$

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

$f (x) = - x^{2} + 2 x + 24 0 = - (x + 4) (x - 6) x = - 4 o r x = 6$

The x-intercepts are $(- 4, 0) a n d (6, 0)$

The graph of the parabola is

03

Step 3. Solution

The solution in interval notation is $(- 鈭� 鈥�, 鈥� - 4) 鈭� (6, 鈥� 鈭� 鈥�)$

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Most popular questions from this chapter

In the following exercises, write as a radical expression.

鈸� r^{\frac{1}{2}} 鈸� s^{\frac{1}{3}} 鈸� t^{\frac{1}{4}}

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