Chapter 11: Q 368 (page 1069)

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

Short Answer

Expert verified

The solution in interval notation is $(- \infty, - 4) \cup (6, \infty)$

Step by step solution

Step 1. Given information

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

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

Step 3. Solution

The solution in interval notation is $(- \infty, - 4) \cup (6, \infty)$

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve graphically

Step 3. Solution

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In the following exercises, ⓐ solve graphically and ⓑ write the solution in interval notation-x2+2x+24<0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve graphically

Step 3. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Decision Maths

Applied Mathematics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

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