Question

The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below. The quadrative function f(x) is represented by the parabola below,

Select all the statements that are true.

The function f(x) has a maximum value at x=4.5.
The function g(x) has a minimum value of 0.
The maximum value of g(x) is twice the maximum value of f(x).
Neither function have a minimum value.

Answer 1

@563blackghost @amistre64 @mathmate @CGGURUMANJUNATH @Michele_Laino

Answer 2

@jango_IN_DTOWN @FrostFlare23 @Ghostgate

Answer 3

@mathstudent55 @FibonacciChick666

Answer 4

@zepdrix @zasharra

Answer 5

alright, let us play the claim/isit true game

Answer 6

The function f(x) has a maximum value at x=4.5.

Is it true?

Answer 7

Yes

Answer 8

really? At \(\color\red{x=4.5}\)?

Answer 9

Oh wait nvm

Answer 10

ok, so do you see where you made your mistake for that one?

Answer 11

yes..

Answer 12

This question I got somewhat right

Answer 13

alright so second claim,

The function g(x) has a minimum value of 0.

(i am going to assume they mean absolute minimum here and not relative)

Is this true?

Answer 14

I put down b and c

Answer 15

And got part of it right

Answer 16

I agree with c

Answer 17

so c and d

Answer 18

well, why d?

Answer 19

So each has a maximum no minimum

Answer 20

why? how can you support that claim?

Answer 21

Well f(x) has y=4.5 pointed up for maximum.

Answer 22

I'll take that as good enough

Answer 23

for maximum that is

Answer 24

and when you say pointed up, you should really use concave instead

Answer 25

concave down* sorry

Answer 26

but I really just want you to convince me on the minimum part

Answer 27

I got the question right after you explained it @FibonacciChick666

Answer 28

uh, np, but you should prove at least to yourself why they have no minimums. Especially since if we restrict g(x) to −3<x<200 we will have a minimum

Answer 29

only option C is correct.@Austin1617