Question

what equation best represented by the graph below ?
A. (x+1)(x-3)(x+2)
B. (x-1)(x+3)(x+2)
C. (x-1)(x-3)(x+2)
D. (x+1)(x+3)(x-2)

Answer 1

Well for starters on the graph where are our zeros?

Answer 2

Or another way of saying this when y=0 what does x equal?
Hint: y=0 at 3 different points

Answer 3

im really confused o.O

Answer 4

Well in order to determine an equation for this graph we have to analyze it
Fine the x-axis on the graph or the line where y=0

Answer 5

is it in the center of the graph ?

Answer 6

Look at the image I have attached. The yellow line is the x axis or where y=0
The boxes are the places where the graph touches the x-axis

Answer 7

so the zeros are -2,1,3

Answer 8

Yaa :)

Answer 9

so it would be D?

Answer 10

Nope and I will explain why

Answer 11

What are zeros mean is that when we plug in -2,1 or 3 into the equation our y value or our answer must be 0
So lets look at equation D
y=(x+1)(x+3)(x-2)
Lets plug in 1
(1+1)(1+3)(1-2)=(2)(4)(-1)=-8
Our answer was 6 and not 0 so obviously this aint the answer

lets take a look at equation C
y=(x-1)(x-3)(x+2)

Lets plug in 1
(1-1)(1-3)(1+2)=(0)(-2)(3)=0

Now lets plug in 3
(3-1)(3-3)(3+2)=(2)(0)(5)=0

Now Lets plug in -2
(-2-1)(-2-3)(-2+2)=(-3)(-5)(0)=0

So when we plug in all our zeros the equation does in fact equal 0

If you noticed you will see that basically for the equation to equal 0 the values in each bracket had to be the same value BUT NEGATIVE
so since our zeroes are -2,3 and 1
So our equation is (x-1)(x-3)(x+2)

Answer 12

thank you so much

Answer 13

I hope you understand it. Its a lil complicating

Answer 14

But if you dont just know that the values in each bracket must have the opposite sign of the zero

Answer 15

okay