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# Algebra Problem

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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)?

Guest Feb 16, 2018
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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

CPhill  Feb 16, 2018
edited by CPhill  Feb 16, 2018

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