Q. 315 For the function, f(x)=8x2-18x+5... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 315 (page 627)

For the function, $f (x) = 8 x^{2} - 18 x + 5$ :
a. Find $x$ , when $f (x) = - 4$ .
b. Use this information to find two points that lie on the graph of the function.

Short Answer

Expert verified

a. The value of $x$ is $\frac{3}{2}$ or $\frac{3}{4}$ when $f (x) = - 4$ .

b. $(\frac{3}{2}, - 4)$ and $(\frac{3}{4}, - 4)$ lie on the graph.

Step by step solution

Part a. Find x when f(x)=-4.

Substituting $f (x) = - 4$ in the given equation,

$f (x) = 8 x^{2} - 18 x + 5 - 4 = 8 x^{2} - 18 x + 5 8 x^{2} - 18 x + 9 = 0 8 x^{2} - 12 x - 6 x + 9 = 0 4 x (2 x - 3) - 3 (2 x - 3) = 0 (2 x - 3) (4 x - 3) = 0$

Using Zero Product Property,

$2 x - 3 = 0$ or

$4 x - 3 = 0$

When $2 x - 3 = 0$ ,

$x = \frac{3}{2}$ .

When $4 x - 3 = 0$ ,

$x = \frac{3}{4}$ .

Checking each value separately,

When $x = \frac{3}{2}$

$f (x) = 8 x^{2} - 18 x + 5 f (\frac{3}{2}) = 8 {(\frac{3}{2})}^{2} - 18 (\frac{3}{2}) + 5 f (\frac{3}{2}) = 18 - 27 + 5 f (\frac{3}{2}) = - 4$

This is true.

When $x = \frac{3}{4}$ ,

$f (x) = 8 x^{2} - 18 x + 5 f (\frac{3}{4}) = 8 {(\frac{3}{4})}^{2} - 18 (\frac{3}{4}) + 5 f (\frac{3}{4}) = \frac{9}{2} - \frac{27}{2} + 5 f (\frac{3}{4}) = - 4$

This is true too.

Part b. Find points that lie on the graph of the function

Since $f (\frac{3}{2}) = - 4$ and $f (\frac{3}{4}) = - 4$ , the points $(\frac{3}{2}, - 4)$ and $(\frac{3}{4}, - 4)$ lie on the graph of the function.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

For the function, $f (x) = 8 x^{2} - 18 x + 5$ :
a. Find $x$ , when $f (x) = - 4$ .
b. Use this information to find two points that lie on the graph of the function.

Short Answer

Step by step solution

Part a. Find x when f(x)=-4.

Part b. Find points that lie on the graph of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

For the function, f(x)=8x2-18x+5:a. Find x, when f(x)=-4.b. Use this information to find two points that lie on the graph of the function.

Short Answer

Step by step solution

Part a. Find x when f(x)=-4.

Part b. Find points that lie on the graph of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the function, $f (x) = 8 x^{2} - 18 x + 5$ :
a. Find $x$ , when $f (x) = - 4$ .
b. Use this information to find two points that lie on the graph of the function.