Whats the domain and range explain in words,

Question

q(x)=-3 (x+2)^2+9?

Answer 1

The function q(x) = - 3(x + 2)² + 9

y = - 3[x - (- 2)]² + 9

The above function represents vertex form of  parbola.

We know that the parabola like curve.

y = - 3[ x - (- 2)]² + 9

Compare it to vertex form of parabola y = a (x - h)² + k.

a = - 3, h = - 2, k = 9

(h, k ) = (x, y)

a is negative number the parabola opens down and has maximum value.

When the parabola opens down it has a maximum point which is the vertex of parabola (- 2, 9).

We know that domain of the function is all possible x values and range is all posible y values.

Parabola domain x =  all real numbers.

In the maximum point y = 9  so the graph of parabola cannot be upper than 9.

Thus the range of function y ≤ 9.

Domain of function is all real numbers.

Range of the function is  {y ∈ R : y  ≤ 9}.