Characteristics of 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) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What does it mean for a quadratic function to have 'zeros'?

Back

Zeros of a quadratic function are the x-values where the function equals zero, also known as the roots of the function.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum value occurs at the vertex if the parabola opens downwards, while the minimum value occurs at the vertex if it opens upwards.

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined using the discriminant (b² - 4ac) from the quadratic formula. If it's positive, there are 2 zeros; if zero, 1 zero; if negative, no real zeros.

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, given by the equation x = -b/(2a).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.