Domain, Range, and Key Features of Quadratics

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 that opens upwards?

Back

The range is y ≥ k, where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is y ≤ k, where k is the y-coordinate of the vertex.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c.

Front

What does the 'a' value in a quadratic function determine?

Back

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

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 = -b/(2a).

Front

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

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

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

Back

The discriminant (b^2 - 4ac) determines the number and type of roots of the quadratic equation.