Hey Can I have help with this question?

[clever quarry]

you can get two points on the graph from the information the first bullet point provides

do you know what those are?

[north wyvern]

Y int -2 and X int (7x-2)?

[clever quarry]

not exactly

if i told you a graph had a y intercept of 5

basically this line

what would the point at the y intercept be, in terms of (x,y) ?

[north wyvern]

0,5

[clever quarry]

right

now if the x intercept is 2/7, what would that point be as (x,y) ?

[north wyvern]

Pretty much a straight line

[clever quarry]

well the x intercept means the graph intersects the x-axis at some point

it intersects at the x value of 2/7

but what is the y value?

think about what the y value of the x axis is

[north wyvern]

0

[clever quarry]

exactly

meaning that the graph will intersect the point (2/7 , 0)

so now you have two intersection points of (0,5) and (2/7,0)

since this line is linear, you should be able to find the slope of the line

[north wyvern]

I just need to find absolute value function do I need slope?

[clever quarry]

you'll have to have some equation y = mx + b, where m is the slope

so yes

[north wyvern]

So for finding slope without a diagram how do i do that

[clever quarry]

im guessing you normally find slope doing "rise over run" right?

[north wyvern]

Yes

[clever quarry]

rise over run is really a visual way to describe the change in the height over a change in distance

meaning the change in y values divided by the change in x values

essentially, if you have two points on the graph, say (x1, y1) and (x2, y2), the slope of the line is given:

m = (y2 - y1) / (x2 - x1)

the "rise" (change in height) over the "run" (change in horizontal distance)

[north wyvern]

2-0 and 0-2/7

[clever quarry]

(0,5) and (2/7,0) are your points

so call (0 , 5) to be (x1,y1)

[north wyvern]

Isnt it 0,2

[clever quarry]

oh it is lmao

[north wyvern]

Y int is 2 on the question

[clever quarry]

sorry

[north wyvern]

All g

[clever quarry]

yes this is correct

what does this simplify to

[north wyvern]

2 over 2/7

[clever quarry]

yes

which equals what?

[north wyvern]

7

[clever quarry]

good, so that is the slope of the line

you can get the equation of the line now by using point slope form

[north wyvern]

so equation is at y=7x + 2

[clever quarry]

great

so there's one more thing, that being the absolute value

do you see what to do?

[north wyvern]

Putting the absolute value sign around the equation?

[clever quarry]

wait also i didnt notice

it shold be -7x

not postivie

because 0 - 2/7 is negative

and you had 2 / (-2/7)

[north wyvern]

Ok I understand that

[clever quarry]

okay, the equation is still right

so now you just need the absolute around -7x + 2

[north wyvern]

So the absolute value is what x cannot equal

[clever quarry]

the abosulte value just makes a negative number positive

[north wyvern]

So is this correct

[clever quarry]

perfect

yep

here is the graph to verify

.286 = 2/7

[north wyvern]

I totally understand if you dont want to but I have a couple more questions if you wanna help

[clever quarry]

i have time for maybe 1 more

sorry

but i can do it

[north wyvern]

Totally understand you are taking time to help without being paid no need to apologize

[clever quarry]

appreciate it

send another we'll do it

[clever quarry]

okay, so what helps is seeing that there exists x intercepts

one at -3, and one at 1

[north wyvern]

Ok and then Maxiumum at 4

[clever quarry]

consider if i gave you the quadratic equation
x^2 + 4x - 5 - 0
to solve for x, you would do
(x+5)(x-1) = 0
and therefore,
x = -5 and x = 1

is this familiar?

[north wyvern]

Been a while since ive done quadratic equations

But I get the solving

[clever quarry]

okay good

so notice the (x+5)(x-1) = 0 part

this correlates to solutions for when the graph intersects the x axis

that being at x = -5, x = 1

[north wyvern]

Yes

[clever quarry]

so that means that if we have solutions at x = -3 and x = 1

[north wyvern]

Im stuck at this part

[clever quarry]

understandable it's tricky

[clever quarry]

note again that these result in x = -5 and 1

so if i have x = -3

that had to of come from (x+3) = 0

[north wyvern]

X cannot equal 3

[clever quarry]

x is negative 3

[north wyvern]

Ok I get x=-3 and +1

[clever quarry]

right

and x = -3 came from (x + 3) = 0

and the +1 from (x - 1) = 0

so therefore, this parabola must have the factors of (x + 3) and (x - 1)

[north wyvern]

Ok

[clever quarry]

note if i plug these factors into a graph, this is the result

the last step is to make sure all y values are greater than 0

[north wyvern]

So just changing them to anything?

[clever quarry]

well all we need to make sure is that
y = (x+3)(x-1)
is always greater than or equal to 0

to do that think about the last problem

[north wyvern]

Do we need slope? n

[clever quarry]

not slope, but absolute brackets

remember that if i have-5, and i do
| -5 |
it equals positive 5

[north wyvern]

So y=(x+3)(x-1) in ab brackets creates the graph

[clever quarry]

yes

this is your answer

and the graph

note that this is the equation without abs brackets

[north wyvern]

I see makes sense

[clever quarry]

note how the part that is below the x - axis in the green is reflected

[north wyvern]

It says I need 2 equations will flipping the signs give the same result

No It wont

[clever quarry]

it wont, good catch

well we have (x+3)(x-1)

so i think if we just foil it is acceptable

or distribute is the better wording

[north wyvern]

X^2 +2X -3

[clever quarry]

good

that in abs brackets is equal to |(x+3)(x-1)|

[north wyvern]

So Y equals that will be my second equation?

[clever quarry]

yep

[north wyvern]

With brackets correct?

[clever quarry]

yes

because you still want y >= 0

[north wyvern]

Thank you very much

[clever quarry]

of course, that's all i got time for

good luck!

[north wyvern]

Wait im not too sure

This gives me this

[clever quarry]

this is right

zoom in and it should look better

note where it hits on the x and y axis is accurate

[north wyvern]

If yoy have the chance can you confirm if the answrs 1/(x-(-2/3)) and 1/((-2/3)-x) are right for this problem

[quaint mango]

.close