# 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

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> 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      Log On

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 Click here to see ALL problems on Quadratic-relations-and-conic-sections 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(6505)   (Show Source): You can put this solution on YOUR website!y=-1/2x sq -3x +2 .. 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 ..