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Determine the quadratic function f whose graph has the following, The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,

 Jul 5, 2022
 #1
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To solve this problem, use vertex form: \(y = a(x-h)^2 +k\), where the vertex occurs at \((h,k)\)

 

Substituting the vertex, we have: \(y = a(x-2)^2 - 1\).

 

Now, plugging in the point \((3,1)\) and solving for a tells us that \(a = 2\)

 

This means that the quadratic in vertex form is \(2(x-2)^2 - 1 = \color{brown}\boxed{2x^2 - 8x + 7}\)

 Jul 5, 2022

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