Evaluate Functions

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

What does the notation f(x) represent?

Back

f(x) represents the output of the function f for the input x.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the input into the function's expression.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, and it can be found using the formula x = -b/(2a).

Front

How do you find the value of a quadratic function at a given x?

Back

Substitute the value of x into the quadratic function's equation and simplify.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and are represented by a straight line, while quadratic functions have a variable rate of change and are represented by a parabola.

Front

How do you find the y-intercept of a function?

Back

The y-intercept of a function is found by evaluating the function at x = 0.

Front

What is the formula for finding the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).