Question

Please help with math

Answer 1

1.
To open these doors, you must match the number and type of solutions for the following two functions in standard form.
f(x) = x2 + 6x – 16
g(x) = x2 +6x + 1

Match the following descriptions of the solutions to each of the functions above.
Hint: they each have their own match.

Two real irrationals solutions
Two real rationals solutions

2. To pass by me, you must tell me how to convert standard form into the general, vertex form... I have a test on it next week.”

Explain how to convert f(x) into the general, vertex form of the equation. Use complete sentences.

Answer 2

@Hero @iambatman can y'all help please. i need this done and it looks like chinese

Answer 3

@hartnn pls

Answer 4

@gnrfan can you find the solutions for f(x)?

Answer 5

first of all, just by looking at f(x) you should immediately know the number of solutions there is

Answer 6

so can you tell how many solutions it has?

Answer 7

3 im guessing :/

Answer 8

no

Answer 9

ok so lets rewrite it properly, you need the ^ to show exponents ok?

Answer 10

yes

Answer 11

so you have f(x) = x^2 + 6x – 16, correct?

Answer 12

on the bottom it shows a bunch of ? do you mean g(x) = x^2 +6x + 1?

Answer 13

you may have to refresh the page, its a glitch, but yeah thats fine,

Answer 14

ok so can you tell me the degree of the polynomial, x^2 + 6x + 1

Answer 15

hold while i solve it

Answer 16

um ok

Answer 17

you dont need to solve it to know the degree

Answer 18

but you have to solve anyways, so might as well i guess, i was just trying to make a point

Answer 19

ph

Answer 20

well its 2

Answer 21

ok the degree is two, so that means it will have 2 roots aka 2 solutions, whatever the degree of the polynomial is, it will have that many roots or solutions

Answer 22

so if you have a polynomial of degree 5, it will have 5 solutions

Answer 23

k, got it

Answer 24

ok so that doesnt help eliminate any answers since both answers have 2 solutions, so yeah now you need to find the roots of g(x) and the roots of f(x)

Answer 25

and you need to determine which has rational solutions and which has irrational solutions

Answer 26

so can you tell me the solutions for f(x) or g(x), ?

Answer 27

hold on

Answer 28

k

Answer 29

what formula do I use to solve these?

Answer 30

you can use the quadratic formula if you like, or you can just set f(x) = 0 and isolate x on one side (which is solving for x)

Answer 31

i recommend you become familiar with both methods

Answer 32

try the second method, first set f(x) = 0

Answer 33

x^2 + 6x - 16 = 0

Answer 34

now isolate x on one side of the equation

Answer 35

so f(x)=x^2+6x-16=0?

Answer 36

yes thats valid, but get rid of the f(x)= part because we dont need it right now

Answer 37

since we know what f(x) = you dont need to write it, its redundant

Answer 38

x=-8,2

Answer 39

pefect, now is -8 a rational number? is 2 a rational number?

Answer 40

yes, i think. I kinda forgot how to tell

Answer 41

ok a rational number can be represented as the ratio of two integers, put it another way, a fraction in which the numerator is an integer and the denominator is an integer

Answer 42

you know what an integer is?

Answer 43

a whole number right

Answer 44

yes its a whole number, more specifically its a whole number that can be positive or negative or 0

Answer 45

ok so can we represent -8 as a ratio of two integers?

Answer 46

yes

Answer 47

yes we can, we can have -8/1, -4/2, 4/-2 8/-1,

Answer 48

cool

Answer 49

so -8 is a rational number

Answer 50

yes

Answer 51

so tell me is sqrt(5) a rational number?

Answer 52

do you mean the sqrt of 5 or just sqrt of 5

Answer 53

by the way i mean 16/-2 and -16/2 instead of 4/-2 and -4/2, sorry for the confusion lol

Answer 54

its rational

Answer 55

square root of 5 is not rational, you cannot represent it as the ratio of two integers

Answer 56

oh, my bad

Answer 57

so how about square root of 25 is that a rational number?

Answer 58

no, not rational

Answer 59

actually square root of 25 is rational, because square root of 25 is either +5 or -5, and +5 can be represented as a ratio of two integers and -5 can be represented as a ratio of two integers

Answer 60

wow, well at least im learning this stuff instead of just being told im wrong by a teacher

Answer 61

lol thats good, i hope you have better teachers in the future, either you or your parents need to talk to your teacher and the principal if necessary to discuss how you are not understanding and the teacher needs to explain it to you

Answer 62

yea, well whats next good sir?

Answer 63

thats what the teacher is paid to do, so if they arent doing their job, they need to quit or be fired

Answer 64

ok so now you can answer, the first question

Answer 65

so what is the answer that matches f(x)

Answer 66

Two real irrationals solutions

or
Two real rationals solutions

Answer 67

remember the solutions were -8 and 2

Answer 68

two real rationals

Answer 69

yep, so you know from the hint that that g(x) must be irrational, since the hint says each one has a match

Answer 70

yup

Answer 71

if you work out the solutions for g(x) you will see they are -3 - 2sqrt(2), and 2sqr(2) - 3

Answer 72

and since we know sqrt(2) is irrational, then -3 -2sqrt(2) must also be irrational, so that confirms our answer for g(x)

Answer 73

yea, can u help with the second part too?

Answer 74

so do you need help with number 2 or you good on that?

Answer 75

ok 1 sec, let me read it

Answer 76

lol

Answer 77

lol

Answer 78

ok so its asking you to write f(x) in vertex form , is that correct?

Answer 79

yup

Answer 80

but i gotta use complete sentences though. i hate that

Answer 81

lol

Answer 82

yeah its kinda annoying but not that hard

Answer 83

so do you know the steps to convert standard form to vertex form?

Answer 84

give me something in standard form and i'll convert it and see if im right

Answer 85

ok so lets use the problem as the example , so i have f(x) = x^2 + 6x - 16, that is currently in standard form, convert it to vertex form

Answer 86

y=(x+3)^2-25

Answer 87

perfect, what method did you use to get that answer

Answer 88

i don't know. I just did the way i was taught

Answer 89

you used completing the square right?

Answer 90

i think so

Answer 91

ok well you dont have to call it completing the square if you dont want to, but yeah you understand how to do it, now can you tell me the first step you took.

Answer 92

first i put it equal to y, then i did the sqr on the right side, then i re-ordered the right side to match the parabola

Answer 93

ok so if you were explaining it to someone trying to teach them, would that make any sense? what you just said, you need to write out sentences that would make sense to somebody just learning how to do it

Answer 94

pretend you are teaching someone how to do it, explain in details each step so they can understand what you mean

Answer 95

k hold on

Answer 96

Set the polynomial equal to y to find the properties of the parabola.
y=x2+6x−16
Complete the square on the right-hand side of the equation.
More Steps
(x+3)2−25
Reorder the right-hand side of the equation to match the standard form of a parabola.
y=(x+3)2−25

Answer 97

@billj5