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What is the maximum value of 4(x + 7)(2 - x) + 4(x + 7)(8 - x), over all real numbers x?

 Jan 29, 2022
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First, we need to simplify \(4(x + 7)(2 - x) + 4(x + 7)(8 - x)\)into \(−8x^2−16x+280\)

 

The maximum value of any quadratic equation is \(c - b^2/4a\), when the quadratic is in \(ax^2 + bx + c\). By subsituting, we find that the maximum value for this equation is \(\color{brown} 288\).

 Jan 29, 2022

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