How do you solve a linear equation like 3x + 7 = 22?	Isolate x: subtract 7 from both sides (3x = 15), then divide by 3. x = 5.
What is slope-intercept form?	y = mx + b, where m is the slope and b is the y-intercept.
How do you find the slope between two points (x1, y1) and (x2, y2)?	Slope = (y2 - y1) / (x2 - x1). Rise over run.
What does it mean when two lines have the same slope but different y-intercepts?	The lines are parallel and the system of equations has no solution.
How do you solve a system of equations by substitution?	Solve one equation for a variable, then substitute that expression into the other equation and solve.
How do you solve a system of equations by elimination?	Multiply equations so one variable has opposite coefficients, add the equations to eliminate it, then solve for the remaining variable.
What is the quadratic formula?	x = (-b +/- sqrt(b^2 - 4ac)) / 2a, for ax^2 + bx + c = 0.
What does the discriminant (b^2 - 4ac) tell you?	Positive = two real solutions, zero = one real solution, negative = no real solutions.
How do you find the vertex of a parabola y = ax^2 + bx + c?	x-coordinate = -b/(2a). Plug that x back into the equation to get the y-coordinate.
What is factored form of a quadratic?	y = a(x - r)(x - s), where r and s are the roots (x-intercepts) of the equation.
How do you factor x^2 + 5x + 6?	Find two numbers that multiply to 6 and add to 5: (x + 2)(x + 3).
What is function notation f(x)?	f(x) names the output of function f for input x. f(3) means substitute 3 for x and evaluate.
If f(x) = 2x + 1, what is f(f(3))?	f(3) = 7, then f(7) = 15.
What does |x - 3| = 7 mean, and how do you solve it?	The distance from x to 3 is 7. Split into two cases: x - 3 = 7 (x = 10) or x - 3 = -7 (x = -4).
How do you solve |2x + 1| < 5?	Rewrite as -5 < 2x + 1 < 5, then solve: -3 < x < 2.
What is the degree of a polynomial?	The highest power of the variable. For example, 4x^3 - x + 2 has degree 3.
What is the Remainder Theorem?	When polynomial p(x) is divided by (x - a), the remainder equals p(a).
How do you solve a linear inequality like -2x + 4 > 10?	Solve like an equation, but flip the inequality sign when multiplying or dividing by a negative. x < -3.
What does the graph of y = |x| look like?	A V-shape with vertex at the origin, opening upward, symmetric about the y-axis.
How do you interpret f(x + 3) vs. f(x) + 3?	f(x + 3) shifts the graph 3 units left. f(x) + 3 shifts the graph 3 units up.
What are extraneous solutions?	Solutions that emerge from algebraic steps (like squaring both sides) but don't satisfy the original equation. Always check answers.