Algebra and Functions Flashcards

Isolate x: subtract 7 from both sides (3x = 15), then divide by 3. x = 5.

y = mx + b, where m is the slope and b is the y-intercept.

Slope = (y2 - y1) / (x2 - x1). Rise over run.

The lines are parallel and the system of equations has no solution.

Solve one equation for a variable, then substitute that expression into the other equation and solve.

Multiply equations so one variable has opposite coefficients, add the equations to eliminate it, then solve for the remaining variable.

x = (-b +/- sqrt(b^2 - 4ac)) / 2a, for ax^2 + bx + c = 0.

Positive = two real solutions, zero = one real solution, negative = no real solutions.

x-coordinate = -b/(2a). Plug that x back into the equation to get the y-coordinate.

y = a(x - r)(x - s), where r and s are the roots (x-intercepts) of the equation.

Find two numbers that multiply to 6 and add to 5: (x + 2)(x + 3).

f(x) names the output of function f for input x. f(3) means substitute 3 for x and evaluate.

f(3) = 7, then f(7) = 15.

The distance from x to 3 is 7. Split into two cases: x - 3 = 7 (x = 10) or x - 3 = -7 (x = -4).

Rewrite as -5 < 2x + 1 < 5, then solve: -3 < x < 2.

The highest power of the variable. For example, 4x^3 - x + 2 has degree 3.

When polynomial p(x) is divided by (x - a), the remainder equals p(a).

Solve like an equation, but flip the inequality sign when multiplying or dividing by a negative. x < -3.

A V-shape with vertex at the origin, opening upward, symmetric about the y-axis.

f(x + 3) shifts the graph 3 units left. f(x) + 3 shifts the graph 3 units up.

Solutions that emerge from algebraic steps (like squaring both sides) but don't satisfy the original equation. Always check answers.