Question

Which of the following is the correct equation for this function?

(will attach graph in a sec as well as the answer choices!)

***Please explain!! idk how to do this. thanks!! :D

Answer 1

here is the graph :)

Answer 2

roots

Answer 3

here are the answer choices
A,B,C,D from top to bottom
thanks!!

Answer 4

what do u mean by roots?

Answer 5

\[x _{1},and,x _{2}\]

Answer 6

like -1 and 3??

Answer 7

so use them in the root formula
\[y=(x-x _{1})(x-x _{2})\]

Answer 8

the other point i use is this??
(1,4)
??

Answer 9

so i get this??
4=(1-(-1))(1-3)
4=(1+1)(-2)
4=(2)(-2)
4=-4
?? wait that doesn't seem right..

Answer 10

so first star with the roots substitution

Answer 11

hold on like this??
y=(x-(-1))(x-3)

Answer 12

sorry i forgot a
in
\[y=a(x-x _{1})(x-x _{2})\]

Answer 13

so y=a(x-(-1))(x-3)
??

Answer 14

and i get y=a(x+1)(x-3)
??

Answer 15

yes

Answer 16

so do i solve for a now?? :O by plugging in values??

Answer 17

yes

Answer 18

okay so i do this?
y=a(x+1)(x-3)
4=a(1+1)(1-3)
4=a(2)(-2)
4=a(-4)
divide both sides by -4
and i get this???
-1=a
??

Answer 19

yes

Answer 20

so this is my answer??
y=-(x+1)(x-3)
so my answer is D. y= -(x+1)(x-3)
???

Answer 21

yes

Answer 22

yay!! thanks so much @jonask :)