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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