Question

Find the coordinates of the vertex and determine whether the graph opens up or down. y=-x^2+x-5

Answer 1

it opens up, because the (x^2) is positive. if it was negative, it would open down. The vertex is as follows:

to find the value of vertex, solve first for when x=o, then when y=0

Answer 2

Actually, note that

y=-x^2+x-5

so it opens downward

y = -(x^2 - x + 1/4) - 5 + 1/4
= -(x - 1/2)^2 - 19/4

Now it should be clear where the vertex lies.