SOLUTION: Hi- this is my problem, that I need help with. State the maxium or minimum value of each quadratic function and name the x-value at which this occurs. f(x)= -2x^2-6x+5 I don't kn

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Question 109226: Hi- this is my problem, that I need help with. State the maxium or minimum value of each quadratic function and name the x-value at which this occurs.
f(x)= -2x^2-6x+5
I don't know where to start, sorry!!!
Thank you in advance for you help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x value at the min/max, use this formula:

x=-b%2F%282a%29

From the equation y=-2x%5E2-6x%2B5 we can see that a=-2 and b=-6

x=%28--6%29%2F%282%2A-2%29 Plug in b=-6 and a=-2


x=6%2F%282%2A-2%29 Negate -6 to get 6


x=%286%29%2F-4 Multiply 2 and -2 to get -4



x=-3%2F2 Reduce


So the min/max occurs at x=-3%2F2 (which is x=-1.5 in decimal form). Lets plug this into the equation to find the min/max


Lets evaluate f%28-1.5%29

f%28x%29=-2x%5E2-6x%2B5 Start with the given polynomial


f%28-1.5%29=-2%28-1.5%29%5E2-6%28-1.5%29%2B5 Plug in x=-1.5


f%28-1.5%29=-2%282.25%29-6%28-1.5%29%2B5 Raise -1.5 to the second power to get 2.25


f%28-1.5%29=-4.5-6%28-1.5%29%2B5 Multiply 2 by 2.25 to get 4.5


f%28-1.5%29=-4.5--9%2B5 Multiply 6 by -1.5 to get -9


f%28-1.5%29=-4.5%2B9%2B5 Negate any negatives


f%28-1.5%29=9.5 Now combine like terms


So the min/max is y=9.5




Notice if you graph the equation y=-2x%5E2-6x%2B5 you get


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