Find the range of the function. Remember that the range is identical to all possible y-values that a function can have.

The function 

f(x) = −x2 + 6

 is a quadratic equation and its graph is a parabola. Since the leading coefficient is negative, the parabola opens downward. Therefore, the y-coordinate of the vertex is the maximum value of the function. The range will be defined as all the values less than or equal to this maximum value.

Comparing the function 

f(x) = −x2 + 6

 to the standard form for a quadratic function, 

f(x) = ax2 + bx + c,

 we have 

a = −1, b = 0, and c = 6.

 Recall that the vertex is given by the following.

(x, y) = 

−b

2a

, f 

−b

2a

Use the values of a, b, and c to calculate the x-coordinate of the vertex.

x

 = 

−b

2a

 = 

−(0)

2(−1)

 = 

0

Now find the y-coordinate of the vertex by substituting 

x = 0

 into the equation and solving for y.

y

 = 

−x2 + 6

 = 

−(0)2 + 6

 = 

The vertex is the following.

(x, y) = 0,  

The y-values of the function are all less than or equal to the y-coordinate of the vertex. So the range of 

f(x) = −x2 + 6

 is given by which of the following?

{y | y ≥ 0}{y | y ≠ 6}    {y | y is a real number}{y | y ≤ 6}{y | y ≥ −6}