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A parabola has two x intercepts at (-2 , 0) and (-3 , 0) and passes through the point (5 , 10). Find the equation of this parabola.

 Jul 9, 2021
 #1
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We  have  that

 

y =  a ( x + 2)  ( x + 3)

 

And since it passes  through  (5, 10)    we can find "a"  thusly

 

10  = a ( 5+2) ( 5 + 3)

 

10  = a  (7)(8)

 

10  = a  (56)

 

a = ( 10 / 56)  =   5 / 28

 

Then we  have  that

 

y =  (5/28) ( x + 2) ( x + 3)

 

y = (5/28)  (x^2  + 5x + 6)

 

y = (5/28)x^2  + (25/28)x  + 15/14

 

 

cool cool cool

 Jul 9, 2021

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