F(x) = 5 + 3x − x2 what is the range

Please use " ^ " to indicate exponentiation:  F(x) = 5 + 3x − x^2.  One way to determine the range of a quadratic function, such as this function is, is to find the vertex.  The y-value of the vertex is the max or the min of the function.

In this case, we have f(x) = -x^2 + 3x + 5, and the associated coefficients are a = -1, b = 3 and c = 5.  The axis of symmetry is x = -b/[2a].

Here, the equation of the axis of symmetry is x = -3/[2*-1), or x = 3/2.

Find the corresponding y value by subbing 3/2 for x in  f(x) = -x^2 + 3x + 5:

f(3/2) = -(3/2)^2 + 3(3/2) + 5  =  -9/4 + 9/2 + 20/4, or 9./4.

Thus, the vertex, representing a maximum, is (3/2, 29/4).

The range is (-infinity, 29/4].

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length