Question

math problem

Answer 1

no clue man sorry

Answer 2

do yk what a probala is ?

Answer 3

sophia got this one

Answer 4

yep

Answer 5

ohhhhh symeterical shii yea this is like oof

Answer 6

@Florisalreadytaken

Answer 7

lets just start with the quadratic form

\[y = a \times (x-b) + c\]

Answer 8

alright

Answer 9

so

a=?

b=?

c=?

Answer 10

-4, -1, -8

Answer 11

Since you can't determine the vertex, you can just use the roots to find the equation

What are the two places where the line crosses the x-axis?

Answer 12

-4 -1

Answer 13

Exactly, -4 and -1

So that means

x = -4
and x = -1


so remember how if we had an equation and we factored it and got something like
(x+2) (x +3) = 0

then your answer was x = -2 and x = -3

so now for our question, we have x = -4 and x = -1

can you put that in the same form?

Answer 14

(x-4) (x-1) = 0

Answer 15

not quite

if it was x-4
then x = 4

same thing x-1 would mean x = 1

but we have x = -4 and x = -1

so just bring those numbers to the other side so that way you have 0 on the other side of the equal sign

Answer 16

im not sure

Answer 17

So look at the example again

(x+2)(x+3) = 0

that means
(x+2) = 0
x = -2

and (x+3) = 0
so x = -3

Answer 18

So again, let's work backwards from this example

if we wanted x = -2 and x = -3

then

x = -2
x + 2 = -2 + 2
x + 2 = 0

and
x = -3
x + 3 = -3 + 3
x + 3 = 0

so we get (x+2)(x+3)

does that make sense?

so what would it be for x = -1 and x = -4

Answer 19

(x+1) (x+4)

Answer 20

There you go!!

Now your question probably wants you to expand it so multiply it out

Answer 21

\( (a+b)(c+d) = ac + bc + ad + bd\)

Answer 22

x^2+5x+4

Answer 23

That's your answer

Answer 24

wait it was backwards though so we have to multiply the entire thing by -1

but we also have to figure out by what factor they're multiplying it

y = -a(x+4)(x+1)

y = -a(x^2 + 5x + 4)

so look at your graph and you see that at (0, 8) is a point that is on the green curve so plug it in

8 = -a(0^2 + 5(0) + 4)

can you solve for a?

Answer 25

im not sure

Answer 26

Let's look at the

(0^2 + 5(0) + 4)

first

what is 0^2 = 0*0 = ??
what is 5 * 0

and then there's + 4

so add it all up

Answer 27

(0+0+4)

Answer 28

4

Answer 29

good so now we have. Remember, we got that -8 because in the graph, the point was (0, -8) so we plugged in x = 0 and we replaced y with -8

-8 = -4a

what is a = ?

Answer 30

4

Answer 31

no

-8 = -4a

divide -4 on both sides

Answer 32

no...?

-8 / -4 =

Answer 33

-2

Answer 34

no, what is a negative number divided by a negative number?

it's positive

Answer 35

2

Answer 36

there you go so that means a = 2

and so we have

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
wait it was backwards though so we have to multiply the entire thing by -1

but we also have to figure out by what factor they're multiplying it

y = -a(x+4)(x+1)

y = -a(x^2 + 5x + 4)

so look at your graph and you see that at (0, 8) is a point that is on the green curve so plug it in

8 = -a(0^2 + 5(0) + 4)

can you solve for a?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 37

and so now we're at

y = -a(x^2 + 5x + 4)

and since a =2

y = -2(x^2 + 5x + 4)

can you distribute -2 inside the parenthesis?

Answer 38

im not sure

Answer 39

just distribute

Answer 40

multiply the -2 with each term

Answer 41

--2x^2-10x-8

Answer 42

that's your final answer

\( -2x^2 -10x-8\)

Answer 43

let the eq. of parabola be y=ax^2+bx+c
\[\because ~it~passes~through (-4,0),(-1,0) and (0,-8)
so
0=16a-4b+c
0=-a-b+c
subtract 17a-3b=0
3b=17a
b=17/3 a
and -8=0a+0b+c
c=-8
16a-4b-8=0
or 4a-b-2=0
4a-b=2 (1)
and -a-b-8=0
or a+b=-8 (2)
add
5a=-6
a=-6/5
from (2)
-6/5+b=-8
b=-8+6/5
b=(-40+6)/5=-34/5
so y=-6/5 x^2-34/5x-8

Answer 44

I have not seen that method before but it's not correct. Your equation doesn't even pass through the point (-1, 0) so there must be some error

https://www.desmos.com/calculator/a78eiz82if

Answer 45

so there may be some mistake in calculation.

Answer 46

let me see

Answer 47

yes i found the mistake
0=a-b+c