SOLUTION: Help me solve by completing the square to change the form of the function
f(x) = -2x^2-2x+2
State the Vertex
State the Point on the line (x,y)
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-> SOLUTION: Help me solve by completing the square to change the form of the function
f(x) = -2x^2-2x+2
State the Vertex
State the Point on the line (x,y)
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Question 1069126: Help me solve by completing the square to change the form of the function
f(x) = -2x^2-2x+2
State the Vertex
State the Point on the line (x,y) Found 2 solutions by Boreal, josmiceli:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! f(x) = -2x^2-2x+2 =-(2x^2+2x-2)
set equal to 0 and move the constant over. We are moving +2 over, so it will be negative on the other side
-(2x^2+2x)=-2
divide by 2 (could do earlier) to make the leading coefficient 1)
-(x^2+x)= -1
take half of the coefficient first power term and square it, adding it to both sides.
-(x^2+x+(1/4))=-1-1/4
make the leading signs positive (can do this earlier
(x^2+x+1/4)=(5/4)
factor
(x+(1/2))^2=5/4
take the square roots of both sides
x+(1/2)=+/- sqrt (5)/2
bring the 1/2 over
x=-1/2+/- sqrt (5)/2 or (-1+/- sqrt (5)/2
The vertex x-value is -b/2a, where b=-2 and a=-2. The vertex x is - (-2/-4)=-1/2
If x= -1/2, f(x)=-2(1/4)+2(1/2)+2=(5/2)
the vertex is at (-1/2, 5/2)
a point on the function is (0,2). Set x equal to 0 for the easiest point to find.
You can put this solution on YOUR website!
When the equation has the form: ,then the
formula for the x-value of the vertex is:
plug this result back into equation
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The vertex is at ( -1/2, 5/2 )
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Here's the plot:
