Algebra 1 covers a wide range of topics and concepts, and there are numerous formulas and equations that are fundamental to the course. Here are some key algebraic formulas and equations typically covered in Algebra 1:

1. Linear Equations:

   • Slope-intercept form of a line: 𝑦=𝑚𝑥+𝑏y=mx+b (where 𝑚m is the slope and 𝑏b is the y-intercept).

   • Point-slope form of a line: 𝑦−𝑦1=𝑚(𝑥−𝑥1)y−y1​=m(x−x1​) (where (𝑥1,𝑦1)(x1​,y1​) is a point on the line and 𝑚m is the slope).

   • Standard form of a linear equation: 𝐴𝑥+𝐵𝑦=𝐶Ax+By=C (where 𝐴A, 𝐵B, and 𝐶C are constants).

2. Quadratic Equations:

   • Standard form of a quadratic equation: 𝑎𝑥2+𝑏𝑥+𝑐=0ax2+bx+c=0 (where 𝑎a, 𝑏b, and 𝑐c are constants and 𝑎≠0a=0).

   • Quadratic formula: 𝑥=−𝑏±𝑏2−4𝑎𝑐2𝑎x=2a−b±b2−4ac​​ (used to solve quadratic equations).

3. Exponents and Radicals:

   • Laws of exponents (e.g., 𝑎𝑚×𝑎𝑛=𝑎𝑚+𝑛am×an=am+n, 𝑎𝑚𝑎𝑛=𝑎𝑚−𝑛anam​=am−n, (𝑎𝑚)𝑛=𝑎𝑚𝑛(am)n=amn, etc.).

   • Simplifying radicals (e.g., 𝑎𝑏=𝑎×𝑏ab​=a​×b​, 𝑎2=∣𝑎∣a2​=∣a∣, etc.).

4. Factoring:

   • Factoring quadratic expressions (e.g., 𝑎𝑥2+𝑏𝑥+𝑐ax2+bx+c can be factored into (𝑑𝑥+𝑒)(𝑓𝑥+𝑔)(dx+e)(fx+g) form).

   • Difference of squares: 𝑎2−𝑏2=(𝑎−𝑏)(𝑎+𝑏)a2−b2=(a−b)(a+b).

   • Perfect square trinomials: 𝑎2+2𝑎𝑏+𝑏2=(𝑎+𝑏)2a2+2ab+b2=(a+b)2, 𝑎2−2𝑎𝑏+𝑏2=(𝑎−𝑏)2a2−2ab+b2=(a−b)2.

5. Systems of Equations:

   • Solving systems of linear equations using substitution or elimination methods.

   • Writing and solving systems of equations from word problems and real-life scenarios.

6. Inequalities:

   • Solving and graphing linear inequalities.

   • Compound inequalities and absolute value inequalities.

7. Functions:

   • Function notation: 𝑓(𝑥)f(x), 𝑔(𝑥)g(x), etc.

   • Evaluating functions and finding function values.

   • Domain and range of functions.

8. Graphing:

   • Plotting points on the coordinate plane.

   • Graphing linear equations and inequalities.

   • Graphing quadratic functions and other basic functions.

These are just a few examples of the formulas and concepts covered in Algebra 1. Depending on the curriculum and standards in your specific course, there may be additional topics and formulas included. It's important to refer to your textbook or curriculum guide for a comprehensive list of formulas and equations relevant to your Algebra 1 course.