You can put this solution on YOUR website! Determine root of the equation f (x) = 5 + 2x - 3x^2 and sketch the position of the parabola
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y=5+2x-3x^2
=-3x^2+2x+5
completing the square to put equation into standard form, y=(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex.
=-3(x^2+(2/3)x+1/9)5+1/3
=-3(x+(1/3))^2+16/3
This is a parabola which opens downward with vertex at (1/3,16/3)
Solving for roots:set y=0 and solve for x
0=-3x^2+2x+5 or
3x^2-2x-5=0
(3x-5)(x+1)
x=5/3
x=-1
see graph of given parabola below:
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