Question

A. Why is the Domain of all Quadratic Functions (-[infinity],[infinity])?

b. What determines the restrictions on the Range of Quadratic Equations?
a) a. The leading coefficient of a quadratic function is always 1. b. The vertex of the quadratic equation.
b) a. The leading coefficient of a quadratic function is always 1. b. The discriminant of the quadratic equation.
c) a. The leading coefficient of a quadratic function is always 2. b. The vertex of the quadratic equation.
d) a. The leading coefficient of a quadratic function is always 2. b. The discriminant of the quadratic equation.

Answer 1

The domain of all quadratic functions is (-∞, +∞), while the range is determined by the vertex.

Step-by-step explanation:

The domain of all quadratic functions is (-∞, +∞). This means that the x-values the quadratic function can take are any real numbers. The reason for this is that a quadratic function is a polynomial function of degree 2, and polynomials have a domain of (-∞, +∞).

The range of a quadratic function is determined by the vertex. The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The range of a quadratic function is the set of all y-values that can be obtained by plugging in the x-values from the domain into the function.

So the correct answer is:

a) The leading coefficient of a quadratic function is always 1.

b) The vertex of the quadratic equation.