Quadratic Attributes

Front

What is the range of a quadratic function?

Back

The range of a quadratic function is the set of all possible output values (y-values). For a parabola that opens upwards, the range is y ≥ k, where k is the y-coordinate of the vertex.

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. It can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax² + bx + c.

Front

How do you find the vertex of a quadratic function?

Back

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

Front

What does it mean if a quadratic function has a minimum value?

Back

A quadratic function has a minimum value if it opens upwards (the coefficient of x² is positive). The minimum value occurs at the vertex of the parabola.

Front

What does it mean if a quadratic function has a maximum value?

Back

A quadratic function has a maximum value if it opens downwards (the coefficient of x² is negative). The maximum value occurs at the vertex of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

You can determine the direction of the parabola by looking at the coefficient 'a' in the standard form. If a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the formula for the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).