Domain and Range 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 in standard form?

Back

The range of a quadratic function in standard form, y = ax^2 + bx + c, depends on the value of 'a'. If 'a' is positive, the range is [k, ∞) where k is the minimum value. If 'a' is negative, the range is (-∞, k] where k is the maximum value.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting this x value back into the function.

Front

What does the vertex represent in the context of a quadratic function?

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the range of the function p(x) = 8x^2 - 16x + 4?

Back

The range of the function p(x) = 8x^2 - 16x + 4 is y ≥ -4.

Front

How do you determine the domain of a quadratic function based on a real-world scenario?

Back

The domain is determined by the context of the problem, such as physical constraints (e.g., time, distance) that limit the values of x.

Front

What is the domain of the function representing the height of a golf ball hit from a tee box?

Back

The domain of the function is 0 ≤ x ≤ 230, where x represents the horizontal distance in yards.

Front

What is the difference between domain and range?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values) that the function can produce.

Front

How can you represent the domain of a function graphically?

Back

The domain can be represented on a graph by indicating the x-values for which the function is defined, often shown as an interval on the x-axis.