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A quadratic function has a vertex point of (3,1) and passes through the point (6,-8).Which equation represents the quadratic equation?

A y=- x^2 + 6x-8
B y=x^2 - 6x +10
C y=- x^2 - 6x-8
D y=- x^2 + 6x -10

 Feb 22, 2020
 #1
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We have  that

 

( y  - k)  = a(  x - h)^2              where (x, y)  is a point on the graph and  (h, k)  is the  vertex.....solving for  "a"  we have

 

(-8 - 1)   = a ( 6  - 3)^2

 

(-9)  = a (3)^2

 

-9  = 9a

 

a = -1

 

So  we  have this

 

y = -1 ( x - 3)^2  + 1      expand and simplify

 

 

y = - (x^2  - 6x + 9)  +  1

 

y = -x^2 + 6x   - 9 + 1

 

y = -x^2  + 6x   - 8

 

Here's the  graph :  https://www.desmos.com/calculator/403szzeeqc

 

 

 

cool cool cool

 Feb 22, 2020

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