Alg 2 Midterm Review Function Forms

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the average rate of change of a function between two points?

Back

The average rate of change between two points (x1, y1) and (x2, y2) is calculated as (y2 - y1) / (x2 - x1).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to combine like terms in an expression?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

Front

How do you convert from vertex form to standard form of a quadratic function?

Back

To convert from vertex form f(x) = a(x-h)² + k to standard form, expand the squared term and simplify to the form ax² + bx + c.

Front

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

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.

Front

What is the formula for the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you identify the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the function equal to zero and solving for x.