SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=-2x^2+2x+9. The x coordinate of the vertex is? (Type a simplified fraction) The

Algebra ->  Equations -> SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=-2x^2+2x+9. The x coordinate of the vertex is? (Type a simplified fraction) The      Log On


   

Question 157345: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=-2x^2+2x+9.
The x coordinate of the vertex is? (Type a simplified fraction)
The y coordinate of the vertex is? (Type a simplified fraction)
The equation of the line of symmetry is x=?
The maximum or minimum of f(x) is?
The value of f(x)=19/2 is maximum or minimum?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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 y=-2x%5E2%2B2x%2B9, we can see that a=-2, b=2, and c=9.


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


x=%28-2%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x=1%2F2 Reduce.


So the x-coordinate of the vertex is x=1%2F2. Note: this means that the axis of symmetry is also x=1%2F2.


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


y=-2x%5E2%2B2x%2B9 Start with the given equation.


y=-2%281%2F2%29%5E2%2B2%281%2F2%29%2B9 Plug in x=1%2F2.


y=-2%281%2F4%29%2B2%281%2F2%29%2B9 Square 1%2F2 to get 1%2F4.


y=-1%2F2%2B2%281%2F2%29%2B9 Multiply -2 and 1%2F4 to get -1%2F2.


y=-1%2F2%2B1%2B9 Multiply 2 and 1%2F2 to get 1.


y=19%2F2 Combine like terms.


So the y-coordinate of the vertex is y=19%2F2.


So the vertex is .


Also, since the leading coefficient is negative, this means that the vertex is at a maximum.

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So using this info we can answer the following:


The x coordinate of the vertex is 1%2F2


The y coordinate of the vertex is 19%2F2


The equation of the line of symmetry is x=1%2F2



The maximum or minimum of f(x) is f%28x%29=19%2F2



The value of f(x)=19/2 is a maximum