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 the form of f(x) = ax^2 + bx + c where a > 0?

Back

The range is all real numbers y such that y ≥ k, where k is the minimum value of the function.

Front

What is the range of a quadratic function in the form of f(x) = ax^2 + bx + c where a < 0?

Back

The range is all real numbers y such that y ≤ k, where k is the maximum value of the function.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

Back

The vertex is at the point (2, -2).

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola that opens upwards if a > 0 and downwards if a < 0.

Front

What is the effect of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and its width (narrower for larger |a| and wider for smaller |a|).

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 of the parabola, given by the equation x = -b/(2a).

Front

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

Back

If a > 0, the function has a minimum value; if a < 0, the function has a maximum value.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.