Question

Function k is a continuous quadratic function that includes the ordered pairs shown in the table. (-1,5), (0,8) (1,9), (2,8) (3,5) (4,0) Over which interval of the domain is the function Increasing? A (1, 00) B. (-00,1) C (-00, 00) D. (-00,9)​

Answer 1

Answer: (-∞ , 1)

Step-by-step explanation:

We know that the quadratic functions only change their "direction" only once.

Now, we can see the data set:

(-1, 5) to (0, 8)

8 is larger to 5, so here we have an increase.

(0, 8) to (1, 9)

9 is larger to 8, so here we have an increase.

(1,9) to (2, 8)

8 is smaller than 9, so here we have a decrease.

And also we can see that f(0) = f(2)

Then our maximum value is right in the middle of 0 and 2.

f(1) = 9 is the maximum value of this function.

This means that in x = 1, the direction of the function changes. We saw that before this point the function was increasing, then after this point the function will decrease forever.

This also means that in all the range x < 1, our quadratic function is increasing.

Then the correct option is: (-∞ , 1)