Quadratic Transformations 2023

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a parabola represent?

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 determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is positive, the function has a minimum value. If 'a' is negative, it has a maximum value.

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 formula x = -b/(2a).

Front

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

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is the y-coordinate of the vertex.

Front

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

Back

The range of a quadratic function that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.