Given the function f(x) = −3^2 + 4x + 6, find f(2) and f(3). choose the statement that is true concerning these two values.
a.) the value of f(2) is the same as the value of f(3).
b.) the value of f(2) cannot be compared to the value of f(3).
c.) the value of f(2) is smaller than the value of f(3).
d.) the value of f(2) is larger than the value of f(3).

D (assuming f(x)=-3x^2+4x+6)

Step-by-step explanation:

Let's find f(2) and f(3).

I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).

f(2) means replace x with 2.

f(2)=-3(2)^2+4(2)+6

Use pemdas to simplify:  -3(4)+4(2)+6=-12+8+6=-4+6=2.

So f(2)=2

f(3) means replace x with 3.

f(3)=-3(3)^2+4(3)+6

Use pemdas to simplify:  -3(9)+4(3)+6=-27+12+6=-15+6=-9

So f(3)=-9

-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4