Key Features 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 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

How do 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 in the function.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of the function crosses the x-axis, which occurs when f(x) = 0.

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 significance of the ordered pair (0, -2) in a quadratic function?

Back

The ordered pair (0, -2) represents the y-intercept of the graph.

Front

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

Back

The ordered pair (3, 0) represents an x-intercept of the graph.

Front

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

Back

The ordered pair (2, -4) represents the vertex of the graph.

Front

How do you determine the vertex from a quadratic equation in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.