Quadratic Function Attributes (AFDA & Alg 2)

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum value); if 'a' is negative, it opens downwards (maximum value).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where 'b' is the coefficient of x and 'a' is the coefficient of x².

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: 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

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 at the vertex; if 'a' is negative, it has a maximum value at the vertex.

Front

What is the formula for finding the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found by substituting the x-coordinate of the vertex into the function: y = a(-b/(2a))² + b(-b/(2a)) + c.