Question

What is this

F(x)=-x^2-3. 7x-6. 5


Find the maximum value
Round to the nearest hundredth

Answer 1

"Find the maximum value" or namely find the value of f(x) at the vertex point, like the one in the picture below.

`\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+-3.7}x\stackrel{\stackrel{c}{\downarrow }}{+-6.5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -3.7}{2(-1)}~~~~ ,~~~~ -6.5-\cfrac{ (-3.7)^2}{4(-1)}\right)\implies \stackrel{maximum~value}{(-1.85~~,~~\stackrel{\downarrow }{-3.08})}`