Key Properties of Quadratics

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a downward-opening quadratic function is y ≤ k, where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens upwards?

Back

The range of an upward-opening quadratic function is y ≥ k, where k is the y-coordinate of the vertex.

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 a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape, which can open upwards or downwards.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if it opens downwards, and this maximum value occurs at the vertex.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value if it opens upwards, and this minimum value occurs at the vertex.