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, known as the domain.

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 variable into the function's expression and simplify.

Front

What is the standard form of a linear function?

Back

The standard form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

How do you find the value of a quadratic function at a specific point?

Back

To find the value of a quadratic function at a specific point, substitute the value of x into the function and simplify.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What is the formula for finding the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function in standard form f(x) = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

Front

How do you determine 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 process for solving a quadratic equation?

Back

A quadratic equation can be solved using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).