Q. 521 In the following exercises, solv... [FREE SOLUTION]

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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. 521 (page 987)

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

Short Answer

Expert verified

The solution of the given inequality is $[- 2, 1]$ .

Step by step solution

Step 1. Given information.

We have:

$- x^{2} - x + 2 鈮� 0$

Step 2. Find the vertex of the function.

$The 鈥� vertex 鈥� of 鈥� an 鈥� up - down 鈥� facing 鈥� parabola 鈥� of 鈥� the 鈥� form 鈥� y = a x^{2} + b x + c 鈥� is 鈥� x_{v} = - \frac{b}{2 a} The 鈥� parabola 鈥� params 鈥� are : a = - 1, 鈥� b = - 1, 鈥� c = 2 x_{v} = - \frac{b}{2 a} x_{v} = - \frac{(- 1)}{2 (- 1)} x_{v} = - \frac{1}{2}$

Substitute $x_{v} = - \frac{1}{2}$ in the original equation to find $y_{v} :$

$y_{v} = \frac{9}{4} Therefore 鈥� the 鈥� parabola 鈥� vertex 鈥� is (- \frac{1}{2}, 鈥� \frac{9}{4})$

Step 3. Find the x-intercept.

Substitute $y = f (x) = 0$ :

$- x^{2} - x + 2 = 0 For 鈥� a 鈥� quadratic 鈥� equation 鈥� of 鈥� the 鈥� form 鈥� a x^{2} + b x + c = 0 鈥� the 鈥� solutions 鈥� are 鈥� x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} For 鈥� a = - 1, 鈥� b = - 1, 鈥� c = 2 x_{1, 鈥� 2} = \frac{- (- 1) 卤 \sqrt{{(- 1)}^{2} - 4 (- 1) 路鈥� 2}}{2 (- 1)} x_{1, 鈥� 2} = \frac{- (- 1) 卤鈥� 3}{2 (- 1)} x = - 2, 鈥� x = 1$

$X 鈥� Intercepts : 鈥� (- 2, 鈥� 0), 鈥� (1, 鈥� 0)$

Step 4. Find the solution by drawing the figure.

Plot the vertex of the function at $(- \frac{1}{2}, 鈥� \frac{9}{4})$ with intercepts then draw the curve passes through the plotted points:

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91影视

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex of the function.

Step 3. Find the x-intercept.

Step 4. Find the solution by drawing the figure.

One App. One Place for Learning.

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91影视

In the following exercises, solve graphically and write the solution in interval notation:-x2-x+2鈮�0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex of the function.

Step 3. Find the x-intercept.

Step 4. Find the solution by drawing the figure.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Pure Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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