SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 3x - 9
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Question 98523: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 3x - 9
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The function has a maximum since the first term has a negative coefficient.
To find the max, you need to find the axis of symmetry first
To find the axis of symmetry, use this formula:
From the equation we can see that a=-1 and b=-3
Plug in b=-3 and a=-1
Negate -3 to get 3
Multiply 2 and -1 to get -2
Reduce
So the axis of symmetry is
So the x-coordinate of the vertex is (which is in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate
Start with the given polynomial
Plug in
Raise -1.5 to the second power to get 2.25
Now combine like terms
So the vertex is (-1.5,-6.75)
So that means the functions highest value is -6.75 which means the functions maximum is -6.75
Notice if you graph the equation you get
Notice the highest y value is -6.75. So our answer is graphically verified.
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