CPhill

We have that

y  = a( x - 1) ( x - 5)

And if the y intercept is 7.....then the point (0, 7) is on the graph.....so we have

7 = a(0 - 1) (0 - 5)   

7 = a (5)     divide both sides by 35

a = 7/5 

So....the function is

y = (7/5)(x - 1) ( x - 5)

y = (7/5) (x^2 -6x + 5)

y = (7/5)x^2 - (42/5)x + 7

See here : https://web2.0calc.com/questions/help_42920

g(2)   means  just putiing 2 into the function and evaluating

4(2)^2 + 2 + 7 =

16 + 2 + 7 =

25

OK....!!!

Note that     f(3) + f(-3)   = f(3 - 3) =   f(0)

So

f(0) =  -12(0)^9 + 0   =   0

(x + 2) ( x - 3)  ≤ 0

Let's solve this

( x + 2) ( x - 3) = 0

Set both factors to 0 and solve for x and we get that   x = - 2  or x = 3

The solutions will come from ( - inf, -2)  or [-2, 3 ] or ( 3, inf )

Note that if we pick a point in [ -2, 3]  (say, 0)....it will make the original inequality true

And the other two intervals will not make the inequality true

So...the solution is [ -2, 3 ]

This is just a tranformation of the absolute value graph   reflected across the x axis and shifted 5 units to the right

See both graphs here : https://www.desmos.com/calculator/mkxvlrzhvd

Ah...an easy one !!!

This point  is the x intercept !!!

NVM

Some numbers are missing, imnotamaster