Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: 9.128 (page 971)

(a) Solve $x^{2} 鈭� 8 x + 12 鈮� 0$ graphically and (b) write the solution in interval notation.

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

$x^{2} 鈭� 8 x + 12 鈮� 0$

Step 2. Graph the function

$f (x) = x^{2} - 8 x + 12 a = 1, b = (- 8), c = 12$

The parabola opens upward as $a$ is positive.

Find the Axis of symmetry.

$f (x) = - \frac{b}{2 a} f (x) = - \frac{(- 8)}{2} f (x) = 4$

Find the Vertex

$f (x) = x^{2} - 8 x + 12 f (4) = {(4)}^{2} - 8 (4) + 12 f (4) = - 4$

Vertex $(4, - 4)$

Step 3. y-intercept

$f (0) = 0^{2} - 8 (0) + 12$

y-intercept is $(0, 12)$

Point symmetric to y-intercept is $(8, 12)$

Find x-intercepts

$f (x) = x^{2} - 8 x + 12 0 = x^{2} - 8 x + 12 0 = (x - 2) (x - 6) x = 2 o r x = 6$

The x-intercepts are $(2, 0) a n d (6, 0)$

The graphical solution is

Step 4. Solution

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

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91影视

(a) Solve $x^{2} 鈭� 8 x + 12 鈮� 0$ graphically and (b) write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graph the function

Step 3. y-intercept

Step 4. Solution

One App. One Place for Learning.

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91影视

(a) Solve x2鈭�8x+12鈮�0 graphically and (b) write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graph the function

Step 3. y-intercept

Step 4. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Discrete Mathematics

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

(a) Solve $x^{2} 鈭� 8 x + 12 鈮� 0$ graphically and (b) write the solution in interval notation.