Precalculus aid » Polynomial functions » Graphs that Polynomial features » write the Equation of a Polynomial duty Based ~ above Its Graph

Which could be the equation because that this graph?

*


*


*


*


*


Explanation:

This graph has zeros at 3, -2, and also -4.5. This method that

*
,
*
, and
*
. That last root is much easier to work with if we think about it together
*
and also simplify it come
*
. Also, this is a negative polynomial, due to the fact that it is decreasing, increasing, decreasing and not the other way around.

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Our equation outcomes from multiply

*
, which results in
*
.


Explanation:

Because there space no x-intercepts, use the type

*
, wherein vertex
*
 is
*
, for this reason
*
,
*
, which gives

*

*

*

*

*


Explanation:

Method 1:

The x-intercepts are

*
. These worths would be obtained if the initial quadratic to be factored, or reverse-FOILed and also the factors were collection equal to zero.

For

*
,
*
. Because that
*
,
*
. This equations determine the result factors and also the resulting function;
*
.

Multiplying the factors and also simplifying, 

*
.

Answer:

*
.

 

Method 2:

Use the kind

*
, whereby
*
is the vertex. 

*
 is
*
, therefore
*
,
*
.

*

Answer:

*

*

*

*

 


Explanation:

The zeros because that this polynomial are

*
.

This way that the factors are same to zero once these values room plugged in for x.

*
main point both political parties by 2

*
for this reason one factor is
*

 

*
multiply both political parties by 3

*
therefore one aspect is
*

 

*
for this reason one element is
*

Multiply these three factors:

*

*
*


Explanation:

The zeros the this polynomial are

*
. This method that the factors equal zero when these values are plugged in.

One variable is

*

One factor is

*

The 3rd factor is identical to

*
. Set equal to 0 and also multiply through 2:

*

*

Multiply these 3 factors:

*

*

The graph is negative since that goes under then up then down, so we have to switch every one of the signs:

*


Explanation:

The zeros that the polynomial room

*
. That way that the factors equal zero once these values space plugged in.

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The an initial factor is

*
or equivalently
*
multiply both political parties by 5:

*

The second and third factors space

*
and also
*

Multiply:

*

*

*

Because the graph goes down-up-down rather of the typical up-down-up, the graph is negative, so change all that the signs:

*


Explanation:

The zeros because that this polynomial are 

*
. That method that the determinants are same to zero once these values space plugged in. 

*
or equivalently
*
multiply both political parties by 4

*
the an initial factor is 
*

 

*
multiply both sides by 3

*
the 2nd factor is
*

 

*
the third factor is
*

 

Multiply the 3 factors:

*

*

*


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