Attributes of Functions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as a coordinate (x, y).

Front

What does the y-value of the vertex represent in a quadratic function?

Back

The y-value of the vertex represents the minimum or maximum value of the function.

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, given by the equation x = h, where (h, k) is the vertex.

Front

How do you find the minimum or maximum value of a quadratic function?

Back

The minimum or maximum value can be found by evaluating the y-value of the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form is given by f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic function indicate?

Back

The coefficient 'a' indicates the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

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

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 > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the slope of a linear function?

Back

The slope is a measure of the steepness of the line, calculated as the change in y over the change in x (rise/run).

Front

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

Back

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