Characteristics of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards (minimum value); if a < 0, it opens downwards (maximum value).

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It represents the maximum or minimum value of the function.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation y = ax² + bx + c.

Front

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

Back

The vertex indicates the maximum or minimum value of the function and the point where the graph changes direction.

Front

What is the maximum value of a quadratic function?

Back

The maximum value is the highest point on the graph of a quadratic function that opens downwards, occurring at the vertex.

Front

What is the minimum value of a quadratic function?

Back

The minimum value is the lowest point on the graph of a quadratic function that opens upwards, occurring at the vertex.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

You can determine this by looking at the 'a' value: if a > 0, it has a minimum value; if a < 0, it has a maximum value.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

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