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Check my answers to 3 questions? I will give a medal and fan

Mathematics
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A function is shown in the table. x g(x) −2 2 −1 0 0 2 1 8 Which of the following is a true statement for this function? A. The function is decreasing from x = 0 to x = 1. B. The function is decreasing from x = −1 to x = 0. C. The function is increasing from x = 0 to x = 1. D. The function is increasing from x = −2 to x = −1.
Would it be c?
correct

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Other answers:

C is correct...you can always think of it as a x,y chart if that helps.
Oh ok thank you to both of you! I have another question..
ok
Two quadratic functions are shown. Function 1: f(x) = 2x2 − 8x + 1 Function 2: x g(x) −2 2 −1 −3 0 2 1 17 Which function has the least minimum value and what are its coordinates? A. Function 1 has the least minimum value and its coordinates are (0, 1). B. Function 1 has the least minimum value and its coordinates are (2, −7). C. Function 2 has the least minimum value and its coordinates are (0, 2). D. Function 2 has the least minimum value and its coordinates are (−1, −3).
fast way to know this is to input 0 into both equation to see its output so...
when input 0 into function 1 we get f(0)=1 while g(0)=2 ....
So A?
yep
yes function 1 ... when x=0 y=1
sorry, I was distracted...go back to the last problem please. with the 2 function, I disagree with A
Yes I think its B, now that I look back at it @stacy.reed08
@pflorido , that's what I got!
how can it be B when they didnt give the x value of x=2 for g(x)?
ok, so looking at the chart I like to think of it as x,y instead of x, g(x). Based on the data given in the table, g(x) has a vertex at -1, -3, because x=-2 and x=0 have the same g(x) value. So the low point for g(x) is the vertex -1, -3
\[f(x)=2(x)^{2}-8(x)+1\]when x=-2 f(-2)=25 and g(x)=2 for the g(x) part they didnt give the function but they state the function output for the given value of x...thats how i see that question...
Water coming out from a fountain is modeled by the function f(x) = −x2 + 8x + 2 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 1 to x = 4 represent? a. The water travels an average distance of 3 feet from 1 second to 4 seconds. b. The water travels an average distance of 2 feet from 1 second to 4 seconds. c. The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds. d. The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.
@LynFran it's really hard to explain on here, but here's my terrible drawing of g(x)...when you graph it, you can clearly see that -1,-3 is the vertex of the parabola....|dw:1439742811899:dw|
well, maybe not clearly from my drawing, but draw it yourself on paper and you'll see :)
@pflorido , for the actual question you're asking, I'd say you can cross off c and d, because they're talking about speed and it says in the problem that f(x) is the height of the water
now just plug in value so you can calculate the rate of change....so what's f(1) and f(4). Once you know those values, you can use them to find rate of change.
So sorry my computer ran out of battery
Ok one second...
f(1) is 9 and f(4) is 18
actually, hold on I'm re-reading the question and I'm not sure we can completely discount c and d yet! but still find the rate of change!
yes, f(1) and f(4) are correct, so now find the rate of change \[\frac{ y-y_{1}}{x-x_{1}}\]
So the coordinates would be (9,0) and (0,18)... I am a little confused @stacy.reed08
nope, you're coordinates are 1,f(1) and 4,f(4)....in other words (1,9) and (4,18)
*your...good thing I'm helping with math and not grammar!
Haha lol
looking at the rate of change equation, I realize I was definitely wrong at first! The y-values , or f(x), represent height, while the x-values represent time so the rate of change is literally distance divided by time...speed :)
So the rate of change is 9/3 or 3
So c?
yes, or still think of it as 3/1...since rate of change is a ratio....3 feet for every 1 second.
yes, c :)
Ok I just have one more.. I know what the answer is but I dont know what the calculation means in context to the problem....
I'll give it a shot!
The function f(x) = −x2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? - I know that the vertex is (24,144).... Part B: Determine the x-intercepts. What do these values mean in the context of the problem? -I know the x-intercepts are (12,0) and (36,0)
This equation is a parabola facing down, so the vertex would be the maximum profit that could be made.
Oh ok and the x-intercepts would be the prices when the profit is at zero, right?
I believe so
Thank you!!!!!! I got a 100%.... Can t thank you any more for all the help you gave me

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