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Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,2), vertical axis of symmetry, and contains the point (1,0).

What is (a , b, c)?

 Feb 16, 2018
 #1
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Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,2), vertical axis of symmetry, and contains the point (1,0).

What is (a , b, c)?

 

In the vertex form, we have

 

y  = a(x - h) +  k   ⇒   (h , k)  =  (3,2)   ....  so.....

 

0  =  a(1 - 3)^2 + 2       subtract 2 from both sides

 

-2  = a (-2)^2

 

-2  = 4a        divide both sides by 4

 

-2/4  =  a  =  - 1/2

 

So we have

 

y = (-1/2)(x -3)^2 + 2

 

y = (-1/2)(x^2 - 6x + 9) + 2

 

y =  (-1/2)x^2 + 3x - 9/2 + 2

 

y  = (-1/2)x + 3x - 5/2   ⇒   (a, b, c)  =  (-1/2, 3, -5/2)

 

Here's the graph  :  https://www.desmos.com/calculator/wxrh0uke2u

 

 

cool cool cool

 Feb 16, 2018
edited by CPhill  Feb 16, 2018

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