Use the information about the graph of a polynomial function to determine the function. assume the leading coefficient is 1 or −1. there may be more than one correct answer. the y-intercept is (0, 9). the x-intercepts are (−3, 0), (3, 0). degree is 2. end behavior: as x → −∞, f(x) → −∞, as x → ∞, f(x) → −∞.

y = -x² + 9

the x-intercepts are x = - 3 and x = 3 hence the factors are

(x + 3 ) and (x - 3 )

polynomial is the product of its factors

y = a(x - 3 )(x + 3) ← ( a is a multiplier )

from the end behaviour the parabola opens down and is a maximum and so the value of a is negative

y = -(x - 3)(x+3) = - (x² - 9 ) = - x² + 9

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers