Consider the polynomial function g(x) = 3x2 + 4x – 5. Find: (a) g(0) (b) g(-2). We will substitute the value in the parentheses on the left-hand side of the equation for the letter on the right-hand side. Then we will follow the rule operations to simplify the right-hand side. To evaluate a polynomial means to find its numerical value, once we know the value of its variable. (a) g(x) = 3x² + 4x – 5 g(0) = 3(0)2 + 4(0) – 5 This is the given function. To find g(0), substitute 0 for x. 4(0)- Evaluate the power. + + 0 - 5 Perform the multiplications. g(0) = g(x) = 3x2 + 4x – 5 g(-2) = 3(-2)² + 4(-2) – 5 (b) This is the given function. To find g(-2), substitute -2 for x. = 3(0) + 4(0)-s Evaluate the power.
Consider the polynomial function g(x) = 3x2 + 4x – 5. Find: (a) g(0) (b) g(-2). We will substitute the value in the parentheses on the left-hand side of the equation for the letter on the right-hand side. Then we will follow the rule operations to simplify the right-hand side. To evaluate a polynomial means to find its numerical value, once we know the value of its variable. (a) g(x) = 3x² + 4x – 5 g(0) = 3(0)2 + 4(0) – 5 This is the given function. To find g(0), substitute 0 for x. 4(0)- Evaluate the power. + + 0 - 5 Perform the multiplications. g(0) = g(x) = 3x2 + 4x – 5 g(-2) = 3(-2)² + 4(-2) – 5 (b) This is the given function. To find g(-2), substitute -2 for x. = 3(0) + 4(0)-s Evaluate the power.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Evaluating Polynomial Functions
Consider the polynomial function \( g(x) = 3x^2 + 4x - 5 \). Find:
(a) \( g(0) \)
(b) \( g(-2) \).
We will substitute the value in the parentheses on the left-hand side of the equation for the letter on the right-hand side. Then we will follow the rules for the order of operations to simplify the right-hand side.
To **evaluate a polynomial** means to find its numerical value, once we know the value of its variable.
#### (a) \( g(0) \)
Given:
\[ g(x) = 3x^2 + 4x - 5 \]
To find \( g(0) \), substitute \( 0 \) for \( x \):
\[ g(0) = 3(0)^2 + 4(0) - 5 \]
\[ g(0) = 3 \cdot 0 + 4 \cdot 0 - 5 \]
\[ g(0) = 0 + 0 - 5 \]
\[ g(0) = -5 \]
#### (b) \( g(-2) \)
Given:
\[ g(x) = 3x^2 + 4x - 5 \]
To find \( g(-2) \), substitute \( -2 \) for \( x \):
\[ g(-2) = 3(-2)^2 + 4(-2) - 5 \]
\[ g(-2) = 3 \cdot 4 + 4 \cdot (-2) - 5 \]
\[ g(-2) = 12 - 8 - 5 \]
\[ g(-2) = -1 \]
### Consider the function \( h(x) = -x^3 + x^2 - 2x + 2 \)
(a) Find \( h(0) \).
To find \( h(0) \), substitute \( 0 \) for \( x \):
\[ h(0) = -(0)^3 + (0)^2 - 2(0) + 2 \]
\[ h(0) = 0 + 0 - 0 + 2 \]
\[ h(0) = 2 \]
(b) Find \( h(-3) \).
To find \( h(-3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c69c300-2450-4b46-97af-8596007e11b9%2F76af1d9f-b670-44c6-a015-d8582433e363%2Fk4t2nkk_processed.png&w=3840&q=75)
Transcribed Image Text:### Evaluating Polynomial Functions
Consider the polynomial function \( g(x) = 3x^2 + 4x - 5 \). Find:
(a) \( g(0) \)
(b) \( g(-2) \).
We will substitute the value in the parentheses on the left-hand side of the equation for the letter on the right-hand side. Then we will follow the rules for the order of operations to simplify the right-hand side.
To **evaluate a polynomial** means to find its numerical value, once we know the value of its variable.
#### (a) \( g(0) \)
Given:
\[ g(x) = 3x^2 + 4x - 5 \]
To find \( g(0) \), substitute \( 0 \) for \( x \):
\[ g(0) = 3(0)^2 + 4(0) - 5 \]
\[ g(0) = 3 \cdot 0 + 4 \cdot 0 - 5 \]
\[ g(0) = 0 + 0 - 5 \]
\[ g(0) = -5 \]
#### (b) \( g(-2) \)
Given:
\[ g(x) = 3x^2 + 4x - 5 \]
To find \( g(-2) \), substitute \( -2 \) for \( x \):
\[ g(-2) = 3(-2)^2 + 4(-2) - 5 \]
\[ g(-2) = 3 \cdot 4 + 4 \cdot (-2) - 5 \]
\[ g(-2) = 12 - 8 - 5 \]
\[ g(-2) = -1 \]
### Consider the function \( h(x) = -x^3 + x^2 - 2x + 2 \)
(a) Find \( h(0) \).
To find \( h(0) \), substitute \( 0 \) for \( x \):
\[ h(0) = -(0)^3 + (0)^2 - 2(0) + 2 \]
\[ h(0) = 0 + 0 - 0 + 2 \]
\[ h(0) = 2 \]
(b) Find \( h(-3) \).
To find \( h(-3)
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