SOLUTION: Determine the maximum or minimum value of the function P(x)= -3x^2+6x+5 I have no idea where to even begin figuring out this problem. I know the answer is either 1 min,max or 8

Algebra ->  Rational-functions -> SOLUTION: Determine the maximum or minimum value of the function P(x)= -3x^2+6x+5 I have no idea where to even begin figuring out this problem. I know the answer is either 1 min,max or 8       Log On


   

Question 207627This question is from textbook
: Determine the maximum or minimum value of the function P(x)= -3x^2+6x+5
I have no idea where to even begin figuring out this problem. I know the answer is either 1 min,max or 8 min, max. Any help will be greatly appreciated. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The min/max is simply the y-coordinate of the vertex.



In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From P%28x%29=-3x%5E2%2B6x%2B5, we can see that a=-3, b=6, and c=5.


x=%28-%286%29%29%2F%282%28-3%29%29 Plug in a=-3 and b=6.


x=%28-6%29%2F%28-6%29 Multiply 2 and -3 to get -6.


x=1 Divide.


So the x-coordinate of the vertex is x=1. Note: this means that the axis of symmetry is also x=1.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


P%28x%29=-3x%5E2%2B6x%2B5 Start with the given equation.


P%281%29=-3%281%29%5E2%2B6%281%29%2B5 Plug in x=1.


P%281%29=-3%281%29%2B6%281%29%2B5 Square 1 to get 1.


P%281%29=-3%2B6%281%29%2B5 Multiply -3 and 1 to get -3.


P%281%29=-3%2B6%2B5 Multiply 6 and 1 to get 6.


P%281%29=8 Combine like terms.


So the y-coordinate of the vertex is y=8.


So the vertex is .


Since the min/max is the y-coordinate of the vertex, this means that the min/max is 8.


Now the question is: is this value a min or is it a max? Since the leading coefficient of y=-3x%5E2%2B6x%2B5 is negative, this means that the value is a max. Graph the equation if you're not sure.