Key Features 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 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 quadratic function?

Back

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

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 are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation f(x) = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0).

Front

What is the significance of the ordered pair (-1, 0) on the graph of a quadratic function?

Back

It is a zero (or root) of the function, meaning the function's value is zero at this point.

Front

What is the significance of the ordered pair (3, 0) on the graph of a quadratic function?

Back

It is an x-intercept, indicating that the function crosses the x-axis at this point.

Front

What is the significance of the ordered pair (2, -4) on the graph of a quadratic function?

Back

It is the vertex of the parabola, representing the minimum or maximum point of the function.

Front

What does it mean for a quadratic function to have an absolute minimum?

Back

An absolute minimum occurs when the vertex of the parabola is the lowest point on the graph, indicating that the function has a minimum value.