Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which f(x) = 0. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of x^2 (a) is positive, indicating that the vertex is a minimum point.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient of x^2 (a) is negative, indicating that the vertex is a maximum point.

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 form of a quadratic function?

Back

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

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex of the parabola. For a function in vertex form, it is the k value in f(x) = a(x - h)^2 + k.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation.