Algebra: Graphs, Functions, and Linear Systems

Front

What is the formula for continuous compound interest?

Back

A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

Front

How do you find the y-intercept of a linear equation in the form Ax + By = C?

Back

To find the y-intercept, set x = 0 and solve for y.

Front

What does the term 'slope' represent in a linear function?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the solution to a system of linear equations?

Back

The solution is the point (x, y) where the two lines intersect, representing the values of x and y that satisfy both equations.

Front

What is the quadratic function and its standard form?

Back

A quadratic function is a polynomial function of degree 2, and its standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point x = a, substitute a into the function and simplify.

Front

What is the process of substitution in solving systems of equations?

Back

Substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form Ax + By = C.