Let f(x)=12x2+4.

the function g(x) is a vertical stretch of f(x) by a factor of 4.

what is the equation of g(x)?

enter your answer in the box.
g(x) =

Step-by-step explanation:

given f(x)=

The function g(x) is a vertical expansion of f(x) by a factor of 4.

when f(x) is vertically expansion  by 'a' f(x)  becomes a f(x)

For vertical expansion by a factor of 4  we multiply f(x) by 4

So

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