Question 109226
To find the x value at the min/max, use this formula:


{{{x=-b/(2a)}}}


From the equation {{{y=-2x^2-6x+5}}} we can see that a=-2 and b=-6


{{{x=(--6)/(2*-2)}}} Plug in b=-6 and a=-2



{{{x=6/(2*-2)}}} Negate -6 to get 6



{{{x=(6)/-4}}} Multiply 2 and -2 to get -4




{{{x=-3/2}}} Reduce



So the min/max occurs at {{{x=-3/2}}} (which is {{{x=-1.5}}} in decimal form). Lets plug this into the equation to find the min/max



Lets evaluate {{{f(-1.5)}}}


{{{f(x)=-2x^2-6x+5}}} Start with the given polynomial



{{{f(-1.5)=-2(-1.5)^2-6(-1.5)+5}}} Plug in {{{x=-1.5}}}



{{{f(-1.5)=-2(2.25)-6(-1.5)+5}}} Raise -1.5 to the second power to get 2.25



{{{f(-1.5)=-4.5-6(-1.5)+5}}} Multiply 2 by 2.25 to get 4.5



{{{f(-1.5)=-4.5--9+5}}} Multiply 6 by -1.5 to get -9



{{{f(-1.5)=-4.5+9+5}}} Negate any negatives



{{{f(-1.5)=9.5}}} Now combine like terms



So the min/max is {{{y=9.5}}}





Notice if you graph the equation {{{y=-2x^2-6x+5}}} you get

{{{drawing(900,900,-11.5,8.5,-0.5,19.5,
grid( 1 ),
graph(900,900,-11.5,8.5,-0.5,19.5, -2x^2-6x+5),

circle(-1.5,9.5,0.05),
circle(-1.5,9.5,0.08)
)}}}


and you can see that the maximum {{{y=9.5}}} occurs at {{{x=-1.5}}}