Answer:

General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Interval Notation
- Function Notation
- Average Rate of Change:

Explanation:
Step 1: Define
h(x) = x² + 3x - 6
[-7, 3] → a = -7, b = 3
Step 2: Find Average
- Substitute in variables [Average Rate of Change]:

- [Average Rate of Change] Substitute in function:
![\displaystyle (3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6])/(3 - -7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/wb2zstxwehx1sh522fauw2y58dhzpv6r5v.png)
- [Average Rate of Change] Simplify:
![\displaystyle (3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6])/(3 + 7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/6xi41yrtdmgjupa6ek11fxkrnfva2b0i96.png)
- [Average Rate of Change] Evaluate exponents:
![\displaystyle (9 + 3(3) - 6 - [49 + 3(-7) - 6])/(3 + 7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/rmlbt0apcqe1fv0fcirihjuu38em5s13h2.png)
- [Average Rate of Change] Multiply:
![\displaystyle (9 + 9 - 6 - [49 - 21 - 6])/(3 + 7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/pjjxau4psqu0o1n4ei8nippvg9buuyx9qx.png)
- [Average Rate of Change] [Brackets] Subtract:
![\displaystyle (9 + 9 - 6 - [28 - 6])/(3 + 7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/2z5ycuyoqe4sai5a015x4bas29q1tfccrn.png)
- [Average Rate of Change] [Brackets] Subtract:

- [Average Rate of Change] Add:

- [Average Rate of Change] Subtract:

- [Average Rate of Change] Subtract:

- [Average Rate of Change] Add:

- [Average Rate of Change] Divide:
