Question

A function is shown in the table.


x g(x)
−2 2
−1 −3
0 2
1 17


Which of the following is a true statement for this function? The function is increasing from x = −2 to x = −1.
The function is increasing from x = 0 to x = 1.
The function is decreasing from x = −1 to x = 0.
The function is decreasing from x = 0 to x = 1.

Answer 1

Hi @kkailyn

This problem seems relatively straightforward. Where exactly are you getting stuck?

Answer 2

Im kind of confused on how to actually answer it. @Nengeni

Answer 3

oh nevermind its c. @Nengeni

Answer 4

@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).

Answer 5

then it has to be B

Answer 6

@Nengeni

Answer 7

@kkailyn

That is correct!

Answer 8

would you mind helping me with two more? @Nengeni

Answer 9

@kkailyn Not at all!

Answer 10

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).

Answer 11

@Nengeni

Answer 12

@kkailyn What do you think the answer is for this question?

Answer 13

@nengeni
B. The last guy that helped me kind of confused me.

Answer 14

B is the correct answer.

Answer 15

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?

Answer 16

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)

Answer 17

Not sure if I asked before... are you familiar with the quadratic formula?

Answer 18

Yes that is what the other person said but he confused me. And ive done it before just not well at it. @Nengeni

Answer 19

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)

Answer 20

In this equation, the vertex represents the maximum profit, which will be found when 25 memberships are sold.