Ntwo or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

f(x) intersects  x-axis at one point (0 , 0)

g(x) intersects x-axis at two points (2-√3 , 0) , (2+√3 , 0)

g(x) is the image of f(x) when f(x) moved right 2 units and

moved down 3 units

Step-by-step explanation:

∵ f(x) = x²

∵ x-intercept means f(x) = 0

∴ x² = 0 ⇒ x = 0

∴ The parabola intersect x-axis at one point (0 , 0)

∵ g(x) = (x - 2)² - 3

∵ x-intercept means g(x) = 0

∴ (x - 2)² - 3 = 0

∴ (x -2)² = 3 ⇒ take square root for both sides

∴ (x - 2) = -√3 ⇒ x = 2 - √3

∴ (x - 2) = √3 ⇒ x = 2 + √3

∴ The parabola intersect x-axis at two points (2-√3 , 0) , (2+√3 , 0)

∵ f(x) = x² , g(x) = (x - 2)² - 3

∴ g(x) is the image of f(x) when :

   f(x) moved right 2 units and moved down 3 units

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

if im not mistaking its

step-by-step explanation: