Q. 438 For the function, f(x)=9x2-18x+5... [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 6: Q. 438 (page 636)

For the function, $f (x) = 9 x^{2} - 18 x + 5$ , (a) find
when $f (x) = - 3$ .(b) Use this information to find two
points that lie on the graph of the function.

Short Answer

Expert verified

(a) The $x$ values for $f (x) = - 3$ are $x = \frac{4}{3}, x = \frac{2}{3}$

(b) Two points that lie on the graph of function are $(\frac{4}{3}, - 3), (\frac{2}{3}, - 3)$

Step by step solution

Step 1. Given

The function is $f (x) = 9 x^{2} - 18 x + 5$

(a) We have to find when $f (x) = - 3$

(b) We also have to find two points that lie on the graph of the function.

Step 2. Find values of x when f(x)=-3

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

So,

role="math" localid="1644661724814" $x = \frac{4}{3}, \frac{2}{3}$

Step 3. Check the value of x at x=43,23

Substitute $x = \frac{4}{3}$ in $f (x)$ ,

$f (x) = 9 x^{2} - 18 x + 5 f (\frac{4}{3}) = 9 {(\frac{4}{3})}^{2} - 18 (\frac{4}{3}) + 5 f (\frac{4}{3}) = 9 (\frac{16}{9}) - 18 (\frac{4}{3}) + 5 f (\frac{4}{3}) = 16 - 24 + 5 f (\frac{4}{3}) = - 3$

Substitute $x = \frac{2}{3}$ in $f (x)$ ,

$f (x) = 9 x^{2} - 18 x + 5 f (\frac{2}{3}) = 9 {(\frac{2}{3})}^{2} - 18 (\frac{2}{3}) + 5 f (\frac{2}{3}) = 4 - 12 + 5 f (\frac{2}{3}) = - 3$

Step 4. Find two points that lie on the graph of the function.

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

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91影视

For the function, $f (x) = 9 x^{2} - 18 x + 5$ , (a) find
when $f (x) = - 3$ .(b) Use this information to find two
points that lie on the graph of the function.

Short Answer

Step by step solution

Step 1. Given

Step 2. Find values of x when f(x)=-3

Step 3. Check the value of x at x=43,23

Step 4. Find two points that lie on the graph of the function.

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91影视

For the function, f(x)=9x2-18x+5, (a) findwhen f(x)=-3.(b) Use this information to find twopoints that lie on the graph of the function.

Short Answer

Step by step solution

Step 1. Given

Step 2. Find values of x when f(x)=-3

Step 3. Check the value of x at x=43,23

Step 4. Find two 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

Pure Maths

Statistics

Probability and Statistics

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

For the function, $f (x) = 9 x^{2} - 18 x + 5$ , (a) find
when $f (x) = - 3$ .(b) Use this information to find two
points that lie on the graph of the function.