Attributes of Quadratics D1

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards (positive) or downwards (negative).

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 downwards or upwards.

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 = -b/(2a).

Front

What is the difference between maximum and minimum values in quadratics?

Back

A maximum value occurs at the vertex of a downward-opening parabola, while a minimum value occurs at the vertex of an upward-opening parabola.

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation f(x) = ax² + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the x-values where the graph intersects the x-axis, found by solving the equation f(x) = 0.

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

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.