Answer:
[tex]\displaystyle -11[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
Algebra I
- Interval Notation
- Average Rate of Change: [tex]\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = -x² - 7x - 8
(1, 3) → a = 1, b = 3
Step 2: Find Average Rate
- Substitute in variables [Average Rate of Change]: [tex]\displaystyle \displaystyle \frac{f(3) - f(1)}{3 - 1}[/tex]
- [Change] Substitute in function: [tex]\displaystyle \displaystyle \frac{[-(3)^2 - 7(3) - 8] - [-(1)^2 - 7(1) - 8]}{3 - 1}[/tex]
- [Change] [Fraction] [Brackets] Evaluate exponents: [tex]\displaystyle \displaystyle \frac{[-9 - 7(3) - 8] - [-1 - 7(1) - 8]}{3 - 1}[/tex]
- [Change] [Fraction] [Brackets] Multiply: [tex]\displaystyle \displaystyle \frac{[-9 - 21 - 8] - [-1 - 7 - 8]}{3 - 1}[/tex]
- [Change] [Fraction] [Brackets] Subtract: [tex]\displaystyle \displaystyle \frac{[-38] - [-16]}{2}[/tex]
- [Change] [Fraction] [Distributive Property] Distribute negative: [tex]\displaystyle \displaystyle \frac{-38 + 16}{2}[/tex]
- [Change] [Fraction] Add: [tex]\displaystyle \displaystyle \frac{-22}{2}[/tex]
- [Change] [Fraction] Divide: [tex]\displaystyle -11[/tex]
