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 the domain of the quadratic function f(x) = x^2?

Back

The domain is all real numbers, {x | x = all real numbers}.

Front

What is the range of the quadratic function f(x) = x^2?

Back

The range is all real numbers greater than or equal to 0, {y | y ≥ 0}.

Front

If a quadratic function opens upwards, what can be said about its range?

Back

The range will always include all values greater than or equal to the minimum point (vertex) of the parabola.

Front

If a quadratic function opens downwards, what can be said about its range?

Back

The range will always include all values less than or equal to the maximum point (vertex) of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on whether it opens upwards or downwards.

Front

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

Back

For a function in the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b/(2a).

Front

What is the effect of the 'a' value in a quadratic function on its graph?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height corresponds to the y-coordinate of the vertex of the quadratic function.