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Hi @kkailyn This problem seems relatively straightforward. Where exactly are you getting stuck?
Im kind of confused on how to actually answer it. @Nengeni
oh nevermind its c. @Nengeni
@kkailyn C is actually the incorrect answer. As you can see from your chart, at x = (-1), the function is at -3, and at x = (0), the function is at 2. Since the function is going from -3 to 2, the function is actually increasing between x = (-1) and x = (0).
then it has to be B
@kkailyn That is correct!
would you mind helping me with two more? @Nengeni
@kkailyn Not at all!
ok well this one i already have answered it but im not quite sure im right. 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? Function 1 has the least minimum value and its coordinates are (0, 1). Function 1 has the least minimum value and its coordinates are (2, −7). Function 2 has the least minimum value and its coordinates are (0, 2). Function 2 has the least minimum value and its coordinates are (−1, −3).
@kkailyn What do you think the answer is for this question?
@nengeni B. The last guy that helped me kind of confused me.
B is the correct answer.
ok now the last one. The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships 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? Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
You can see from the chart that function #2 has a minimum value of (-1,-3). We know this because the x values on either side of -1, -2 and 0, provide us with y values that are greater than -3. Now that we know what the minimum value is for function #2, we need to find the minimum for function #1. We can do this by using the first bit of the quadratic formula (-b/2a). Plugging in function #1 gives us (8/4) or 2. This represents the x value of the vertex. Plugging 2 into function #1 gives us an answer of -7, or a vertex of (2,-7). Now that we know both vertices, we can see that, since -7 is smaller than -3, function #1 has the least minimum value, occurring at (2,-7)
Not sure if I asked before... are you familiar with the quadratic formula?
Yes that is what the other person said but he confused me. And ive done it before just not well at it. @Nengeni
Since you know the quadratic formula, the first part is relatively simple. Once again, using the first bit of the quadratic formula (-b/2a) we can find the x value of the vertex. Let's do that... (-50/-2) = 25. This is the x value so let's plug it into the equation and find the corresponding y value. f(25) = -25^2 + 50*25 - 264 = 625 + 1250 - 264 = 1611. The vertex can be found at (25,1611)
In this equation, the vertex represents the maximum profit, which will be found when 25 memberships are sold.