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Find a formula for the polynomial of least degree its x-intercepts are 0 and -2 and the graph goes through the point (2, -64)

 Apr 6, 2020
 #1
avatar+932 
+2

Given the x-intercepts, we can set up and equation in the form y=a(x-x1)(x-x2) where x1 and x2 are the x-intercepts. In order to find the equation of the graph, we need to solve for a. Filling out the numbers we get y=a(x-0)(x-(-2)). We then plug in the point (2, -64) as X and Y to get -64=a(2-0)(2+2). That simplifies into a=-8. The equation then turns into -8x^2-16x which is our answer. Graph it to check if it works.

 

Hope it helps!

 Apr 6, 2020
 #2
avatar+111329 
+2

The roots  are    x = 0  and  x = -2

 

So....we have  this form

 

y = a (x)( x + 2)       and we can find  a    as  follows

 

 

-64  = a (2)( 2+2)

 

-64  = a ( 2)(4)

 

-64  = a (8)    divide  both sides  by  8

 

-8  = a

 

So....the form is 

 

y  = -8 (x) ( x + 2)       simplify

 

y = -8 ( x^2 + 2x)

 

y = -8x^2  - 16x

 

 

cool cool cool

 Apr 6, 2020

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