Domain and Range: Quadratic

Front

What is the definition of Domain in a function?

Back

The set of all possible input values (x-values) for a function.

Front

What is the definition of Range in a function?

Back

The set of all possible output values (y-values) for a function.

Front

What is a Quadratic Function?

Back

A function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the Vertex of a parabola represent?

Back

The highest or lowest point on the graph of a quadratic function.

Front

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

Back

If the coefficient of x² (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 vertex form of a quadratic function?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

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 is the significance of the y-intercept in a quadratic function?

Back

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

Front

How do you find the domain of a quadratic function?

Back

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

Front

How do you find the range of a quadratic function that opens upwards?

Back

The range is from the y-coordinate of the vertex to positive infinity, expressed as [k, ∞) where (h, k) is the vertex.