Q. 316 For the function, f(x)=18x2+15x-... [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. 316 (page 627)

For the function, $f (x) = 18 x^{2} + 15 x - 10$ :
a. Find $x$ , when $f (x) = 15$ .
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 $- \frac{5}{3}$ or $\frac{5}{6}$ when $f (x) = 15$ .

b. $(- \frac{5}{3}, 15)$ and $(\frac{5}{6}, 15)$ lie on the graph.

Step by step solution

Part a. Find x when f(x)=15.

Substitute $f (x) = 15$ in the given equation,

$f (x) = 18 x^{2} + 15 x - 10 15 = 18 x^{2} + 15 x - 10 18 x^{2} + 15 x - 25 = 0 18 x^{2} + 30 x - 15 x - 25 = 0 6 x (3 x + 5) - 5 (3 x + 5) = 0 (3 x + 5) (6 x - 5) = 0$

Using Zero Product Property,

$3 x + 5 = 0$ or

$6 x - 5 = 0$ .

When $3 x + 5 = 0$ ,

$x = - \frac{5}{3}$

When $6 x - 5 = 0$ ,

$x = \frac{5}{6}$ .

Checking each value separately,

when $x = - \frac{5}{3}$ ,

$f (x) = 18 x^{2} + 15 x - 10 f (- \frac{5}{3}) = 18 {(- \frac{5}{3})}^{2} + 15 (- \frac{5}{3}) - 10 f (- \frac{5}{3}) = 50 - 25 - 10 f (- \frac{5}{3}) = 15$

This is true.

When $x = \frac{5}{6}$ ,

$f (x) = 18 x^{2} + 15 x - 10 f (\frac{5}{6}) = 18 {(\frac{5}{6})}^{2} + 15 (\frac{5}{6}) - 10 f (\frac{5}{6}) = \frac{25}{2} + \frac{25}{2} - 10 f (\frac{5}{6}) = 15$

This is true too.

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

Since $f (- \frac{5}{3}) = 15$ and $f (\frac{5}{6}) = 15$ , the points $(- \frac{5}{3}, 15)$ and $(\frac{5}{6}, 15)$ lie on the graph of the function.

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91影视

For the function, $f (x) = 18 x^{2} + 15 x - 10$ :
a. Find $x$ , when $f (x) = 15$ .
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)=15.

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

One App. One Place for Learning.

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91影视

For the function, f(x)=18x2+15x-10:a. Find x, when f(x)=15.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)=15.

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

Geometry

Pure Maths

Applied Mathematics

Mechanics Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For the function, $f (x) = 18 x^{2} + 15 x - 10$ :
a. Find $x$ , when $f (x) = 15$ .
b. Use this information to find two points that lie on the graph of the function.