Quadratic Domain and Range

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

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 minimum value of the function, typically expressed as [k, ∞) where k is the minimum value.

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 maximum value of the function, typically expressed as (-∞, k] where k is the maximum value.

Front

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

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

Front

What are x-intercepts of a quadratic function?

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What does it mean for a quadratic function to be in vertex form?

Back

Vertex form is expressed as f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the range of a quadratic function given its vertex?

Back

If the parabola opens upwards, the range is [k, ∞) where k is the y-coordinate of the vertex. If it opens downwards, the range is (-∞, k].

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h in vertex form.

Front

How can you identify the domain of a quadratic function from its graph?

Back

The domain of a quadratic function is always all real numbers, as the graph extends infinitely in both directions along the x-axis.