Quadratic Functions Vocabulary

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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

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 downwards or upwards.

Front

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

Back

If the coefficient 'a' is positive, the parabola opens upwards and has a minimum value. If 'a' is negative, it opens downwards and has a maximum value.

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 formula 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.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the input values.

Front

How can you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola; larger absolute values of 'a' make the parabola narrower.