SOLUTION: Find the vertex, focus, and directrix without completing the square, and deteremine opens upward or downward. y=-1/2x sq -3x +2 I've determined it will open downward, but am conf

Question 406287: Find the vertex, focus, and directrix without completing the square, and deteremine opens upward or downward.
y=-1/2x sq -3x +2
I've determined it will open downward, but am confused on how to get the rest of the answers....
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
y=-1/2x sq -3x +2
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If you do not complete the square to solve, you can use another method using the formula, x-coordinate of the vertex=-b/2a.
In the given equation, a=-(1/2), b=-3
x=-(-3)/2(-1/2)=3/-1=-3
solving for y=-(1/2)(-3)^2 -3(-3) +2
y=-9/2+9+2=13/2
This is a parabola that opens downward.
Coordinates of the vertex are (-3,13/2)
Axis of symmetry, x=-3
Set x=0 to find the y-intercept=2
Set y=0 and solve for x-intercepts by factoring or by using the quadratic formula.
x=[-(-3)+-sqrt(3^2-4(-1/2)(2)]2*(-1/2)
x=(3+sqrt(13)/-1 or (3-sqrt(13)/-1
x=-6.6 or x=.61
see the graph below of the given equation
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