Quadratics: Characteristics, Transformations and graphings

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 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 whether it opens upwards or downwards.

Front

How do you find the axis of symmetry of a parabola?

Back

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

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards when the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is negative.

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 a maximum value in the context of a quadratic function?

Back

The maximum value is the highest point on the graph of a downward-opening parabola.

Front

What is a minimum value in the context of a quadratic function?

Back

The minimum value is the lowest point on the graph of an upward-opening parabola.

Front

How do you translate the graph of f(x) = x² horizontally?

Back

To translate the graph horizontally, adjust the x-value in the function: f(x) = (x - h)² translates h units to the right, while f(x) = (x + h)² translates h units to the left.