Question

Is the​ equation's graph opening up or​ down?

Answer 1

Answer:

Step-by-step explanation:

Your "y=2xsquared-12x+10" translates into y = 2x^2 - 12x + 10.  This factors into y = 2(x^2 - 6x + 5).

Setting this = to 0 results in y = 2(x - 5)(x - 1) = 0, so that the x-intercepts are (5,  0) and (1, 0).  The x-coordinate of the vertex lies halfway between x = 1 and x = 5, that is, at x = 3.  Using synthetic division to evaluate y = 2x^2 - 12x + 10 at x = 3, we get

3    2    -12    10

              6    -18

     ------------------

      2     -6     -8

Therefore, the vertex is located at (3, -8).

Setting x = 0 results in the y-intercept:  y = 2(0)^2 - 12(0) + 10 => (0, 10)