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The quadratic ax^2+bx+c can be expressed in the form 2(x-4)^2+8. When the quadratic 3ax^2+2bx+c is expressed in the form n(x-h)^2+k, what is h?

 Jun 29, 2022
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Convert vertex form to standard form: \(2(x-4)^2 + 8 = 2(x^2 - 8x + 16) + 8 = 2x^2- 16x + 40\)

 

This means that \(a = 2\)\(b = -16\), and \(c = 40\). So, the quadratic we need to convert to vertex form is \(6x^2 - 32x + 40\).

 

Note that in vertex form (which we need to convert it to), the vertex occurs at \((h,k)\).

 

This means we need to find the x-coordinate of the vertex, which occurs at \({-b \over 2a}={32 \over 12} = \color{brown}\boxed{8 \over 3}\)

 Jun 29, 2022

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