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Find a formula for quadratic function whose graph has its vertex at (1,4) and its y-intercept at y=-6

 Apr 6, 2020
 #1
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We have  the form

 

y = ax^2  + bx  +  c

 

If  the y intercept is  -6,   then  c   = -6

 

The x coordinate  of the vertexx is given by  -b/[2a]   = 1  which  implies  that  - b  = 2a  ⇒ b = -2a

 

And     we  know that

 

4  = a^(1)^2  - 2a (1)  - 6    simplify

 

4 = a - 2a  - 6     add 6 to both sides

 

10  =  -a      ⇒   a   =  -10    and b  (-2)(-10)   = 20

 

So....the  function  is

 

y = -10x^2  + 20x  - 6

 

 

cool cool cool

 Apr 6, 2020

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