Simplify: (-x^2 - 7x + 10) - (8x^2 + 8x + 8).

-(9 x^2 + 15 x - 2)

Step-by-step explanation:

Simplify the following:

-(8 x^2 + 8 x + 8) - x^2 - 7 x + 10

Factor 8 out of 8 x^2 + 8 x + 8:

-x^2 - 7 x + 10 - 8 (x^2 + x + 1)

-8 (x^2 + x + 1) = -8 x^2 - 8 x - 8:

-8 x^2 - 8 x - 8 - x^2 - 7 x + 10

Grouping like terms, -x^2 - 8 x^2 - 7 x - 8 x - 8 + 10 = (-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8):

(-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8)

-x^2 - 8 x^2 = -9 x^2:

-9 x^2 + (-7 x - 8 x) + (10 - 8)

-7 x - 8 x = -15 x:

-9 x^2 + -15 x + (10 - 8)

10 - 8 = 2:

-9 x^2 - 15 x + 2

Factor -1 out of -9 x^2 - 15 x + 2:

 -(9 x^2 + 15 x - 2)

f(x) has slope (10-0)/(10-5) = 10/5 = 2

and intercept y - mx = 0 - 5(2) = -10 so f(x) = 2x - 10

g(x) has slope (10-0)/(2+3) = 2 and intercept y - mx = 10 - 2*2 =6

so g(x) = 2x + 6

Part A) shift left 2 units or shift up 10 units

Part B) k=-2 and k=10

Part C) g(x)=f(x+2) or g(x)=f(x)+10