Key Features of Quadratic Functions

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers.

Front

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

Back

The range is y ≥ k, where k is the minimum value (y-coordinate of the vertex).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the function, represented as (h, k) in the vertex form y = a(x - h)² + k.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set the function equal to zero and solve for x.

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 the function at 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 equation x = h, where (h, k) is the vertex.

Front

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

Back

A quadratic function has a minimum value if it opens upwards (a > 0), and the minimum value occurs at the vertex.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if it opens downwards (a < 0), and the maximum value occurs at the vertex.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

The direction of the parabola is determined by the coefficient 'a' in the standard form y = ax² + bx + c: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.