Question

Functions f(x) and g(x) are described as follows:

f(x) = −5x2 + 9

x g(x)
0 0
1 4
2 8
3 4
4 0


Which statement best compares the maximum value of the two functions?

It is equal for both functions.
It is 3 units higher for f(x) than g(x).
It is 3 units lower for f(x) than g(x).
It is 1 unit higher for f(x) than g(x).

Answer 1

Well have you found the max values of both functions?

Answer 2

f is already in vertex form

Answer 3

no i havent.

Answer 4

\[f(x)=a(x-h)^2+k \\ \text{ if } a \text{ is negative then } k \text{ is a \max} \\ \text{ if } a \text{ is positive then } k \text{ is a \min}\]

Answer 5

And for g you just have to look for which g(x) value is the highest and that is the max

Answer 6

I am very confused i am just learning this stuff.

Answer 7

compare the following two things:
\[f(x)=a(x-h)^2+k \\ f(x)-5(x-0)^2+9\]
is there anyway you can determine what k is

Answer 8

everything is lined up where it should be
a is -5
h is 0
k is...

Answer 9

9?

Answer 10

yes

Answer 11

now followed what I said above

Answer 12

since a is negative then k is a max

Answer 13

you did have a is -5
so k=9 is your max

Answer 14

9 is the max value of f

Answer 15

can you look at your list of g(x) values and just say what the highest number is listed there

Answer 16

8?

Answer 17

yes so the max of g is 8

Answer 18

are you able to answer the question now?

Answer 19

SO the answer is c?

Answer 20

so you think 9 is 3 units less than 8?

Answer 21

OH

Answer 22

Its D.

Answer 23

yes 9 is one more than 8

Answer 24

if you don't know the vertex form of a parabola you could graph the function given to you next time and just go to the peak of the mountain and find the highest y value there

Answer 25

Can you help with 1 more?

Answer 26

I can try

Answer 27

Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Square with an inner frame with height of 2ft on the left frame and width of 3ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.
x2 + 14x − 2 = 0
2x2 + 10x − 7 = 0
3x2 + 12x − 7 = 0
4x2 + 10x − 1 = 0

Answer 28

let me get the graph

Answer 29

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