SOLUTION: Graph f(x)=x^4-4x^2 First find the x-intercepts then evaluate f(-3),f(-1),f(1),f(3)

Question 113794: Graph f(x)=x^4-4x^2

First find the x-intercepts then evaluate f(-3),f(-1),f(1),f(3)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given function

Factor out the GCF

Factor using the difference of squares to get

Now to find the x-intercepts, set equal to zero and solve for x

Break up the equation using the zero product property
, or

, or Solve for x in each case

So our solutions are , or which means the x-intercepts are (0,0), (2,0), and (-2,0)

Notice if we graph, we get

and we can see that the x-intercepts are (0,0), (2,0), and (-2,0)

------------------------------------------------------------------------

Let's evaluate
Start with the given function.

Plug in . In other words, replace each x with -3.

Evaluate to get 81.

Evaluate to get 9.

Multiply -4 and 9 to get -36

Now combine like terms

-----------Now let's evaluate another value---------
Let's evaluate
Start with the given function.

Plug in . In other words, replace each x with -1.

Evaluate to get 1.

Evaluate to get 1.

Multiply -4 and 1 to get -4

Now combine like terms

-----------Now let's evaluate another value---------
Let's evaluate
Start with the given function.

Plug in . In other words, replace each x with 1.

Evaluate to get 1.

Evaluate to get 1.

Multiply -4 and 1 to get -4

Now combine like terms

-----------Now let's evaluate another value---------
Let's evaluate
Start with the given function.

Plug in . In other words, replace each x with 3.

Evaluate to get 81.

Evaluate to get 9.

Multiply -4 and 9 to get -36

Now combine like terms

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