Chapter 9: 9.128 (page 971)

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

Short Answer

Expert verified

The solution in interval notation is $(- \infty, 2] \cup [6, \infty)$

Step by step solution

Step 1. Given information

$x^{2} - 8 x + 12 \geq 0$

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 $(- \infty, 2] \cup [6, \infty)$

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(a) Solve $x^{2} - 8 x + 12 \geq 0$ 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

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(a) Solve x2−8x+12≥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

Logic and Functions

Statistics

Discrete Mathematics

Calculus

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

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