Domain and Range of Quadratic Functions

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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.

Front

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

Back

The range is determined by the vertex of the parabola; if the vertex is at (h, k), the range is k ≤ y < ∞.

Front

How do you determine the range of a quadratic function that opens downwards?

Back

The range is determined by the vertex of the parabola; if the vertex is at (h, k), the range is -∞ < y ≤ k.

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 it opens upwards or downwards.

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 is the maximum height of a projectile in relation to quadratic functions?

Back

The maximum height corresponds to the vertex of the parabola when modeling the height of a projectile over time.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts (or roots) are the points where the graph intersects the x-axis, indicating the values of x for which f(x) = 0.