SOLUTION: Find the x-intercepts, y-intercepts and the vertex of g(x)=-3x^2+6x+1

Question 460960: Find the x-intercepts, y-intercepts and the vertex of g(x)=-3x^2+6x+1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the x-intercepts, y-intercepts and the vertex of g(x)=-3x^2+6x+1
..
g(x)=-3x^2+6x+1
2nd degree equations are parabolas and the standard form for parabolas is: y=A(x-h)^2+k with (h,k) being the (x,y) coordinates of the vertex. A is a multiplier which affects the steepness of the curve.
completing the square
y=-3(x^2-2x+1)+1+3
y=-3(x-1)^2+4
Vertex:(1,4)
..
y-intercept
x=0
y=1
..
x-intercept
y=0=-3(x-1)^2+4
-3(x-1)^2=-4
(x-1)^2=-4/-3=4/3
x-1=√4/√3=2/√3
x=1�2/√3=1�1.1547
x=2.1547
or
x=.1547
see graph below as a visual check on the answers

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