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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 366 (page 977)

In the following exercises, 鈸� solve graphically and 鈸� write the solution in interval notation $x^{2} - 6 x + 8 鈮� 0$

Short Answer

Expert verified

The solution in interval notation is $(- 鈭� 鈥�, 鈥� 2] 鈭� 鈥� [4, 鈥� 鈭� 鈥�)$

Step by step solution

01

Step 1. Given information

$x^{2} - 6 x + 8 鈮� 0$

02

Step 2. Solve graphically

The quadratic equation in standard form.

$x^{2} - 6 x + 8 鈮� 0$

Graph the function $f (x) = x^{2} - 6 x + 8$

The parabola opens upward.

Find the line of symmetry

$x = - \frac{b}{2 a} x = 3$

Find the vertex.

$f (x) = x^{2} - 6 x + 8 f (3) = - 1$

vertex is $(3, - 1)$

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

$f (x) = x^{2} - 6 x + 8 0 = (x - 2) (x - 4) x = 2 o r x = 4$

The x-intercepts are $(2, 0) a n d (4, 0)$

The graph of the parabola is

03

Step 3. Solution

The solution in interval notation is $(- 鈭� 鈥�, 鈥� 2] 鈭� 鈥� [4, 鈥� 鈭� 鈥�)$

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Most popular questions from this chapter

Determine the number and type of solutions to each quadratic equation.

$a) b^{2} + 7 b - 13 = 0 b) 5 a^{2} - 6 a + 10 = 0 c) 4 r^{2} - 20 r + 25 = 0$

Solve by using the Quadratic Formula: $25 t^{2} - 40 t = - 16$

In the following exercise, solve by completing the square.

$x^{2} - 20 x = 21$

Solve quadratic equation $9 y^{2} + 12 y + 4 = 9$ using square root property

Identify the most appropriate method to use to solve each quadratic equation.

$a) 8 a^{2} + 3 a - 9 = 0 b) 4 b^{2} + 4 b + 1 = 0 c) 5 c^{2} = 125$

See all solutions

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