Question

MEDAL FOR RIGHT ANSWER!!!

Answer 1

A function is shown in the table.

x g(x)
−3 17
−1 −3
0 −4
2 13
Which of the following is a truestatement for this function? (5 points)
The function is increasing from x = −3 to x = −1.
The function is increasing from x = −1 to x = 0.
The function is decreasing from x = 0 to x = 2.
The function is decreasing from x = −3 to x = −1.

Answer 2

you can find the minimum value of a quadratic function by using the formula
-b/2a if we assume that the equation is given in the form y=ax^2 + bx +c
then, try to plot the values of the second function roughly on a graph paper or even a simple paper will do good with some estimation and then, you can get the answer

Answer 3

assume that we have a quadratic equation of the form y=ax^2 + bx + c
now, compare the equation y=ax^2 + bx + c (we call it the standard equation)
to the given equation, i.e. f(x) = 3x2 + 6x + 7
so we get a=3, b=6, c=7
now put the values of a abd b in the formula that i have specified in the above post

Answer 4

ok so the answer would be...?

Answer 5

@Graceland00 are you able to find the slope of the line through any two points? Are you familiar with the slope formula?

Answer 6

y=mx+b?

Answer 7

I'm referring to this slope formula
\[\Large m = \frac{y_2-y_1}{x_2-x_1}\]

Answer 8

ohhh

Answer 9

does it look familiar?

Answer 10

yes

Answer 11

focus on the two rows

−3 17
−1 −3

so we have the two points (-3,17) and (-1,-3)

what is the slope of the line through the two points (-3,17) and (-1,-3) ?

Answer 12

I'm not very sure

Answer 13

Let
(x1,y1) = (-3,17)
and
(x2,y2) = (-1,-3)


Plug these coordinates into the slope formula to get

\[\Large m = \frac{y_2-y_1}{x_2-x_1}\]
\[\Large m = \frac{-3-17}{-1-(-3)}\]
\[\Large m = \frac{-3-17}{-1+3}\]
\[\Large m = ???\]
I'll let you simplify

Answer 14

m=-17/2

Answer 15

-3-17 is equal to what?

Answer 16

-17

Answer 17

-20

Answer 18

sorry

Answer 19

that's fine

Answer 20

yes, -3-17 is equal to -20

Answer 21

so
\[\Large m = \frac{-3-17}{-1+3}\]
\[\Large m = \frac{-20}{2}\]
\[\Large m = -10\]
slope = -10

Answer 22

ok

Answer 23

what next

Answer 24

The slope from x = -3 to x = -1 is \(\large -10\)
Since the slope is negative, this means the function is \(\large \text{Decreasing}\) from x = -3 to x = -1

Answer 25

thank you!

Answer 26

choice A says `The function is increasing from x = −3 to x = −1.` which is the opposite of what I just posted. So choice A is incorrect

Answer 27

you'll go through the other sub-intervals and see which are increasing or decreasing. Compare what you get to the answer choices

Answer 28

ok thanks of the help! i really appreciate it

Answer 29

no problem