Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.

y = -2x^2 + x- 3

Question

Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.

y = -2x^2 + x- 3

anonymous · Answer

The x axis can be described as y=0 , so to find which points these two functions have in common, set them equal to each other, that is, plug in 0 for y (remember what solutions you get when you have an x^2 term).  To find the vertex, notice constant term -3.  What does this imply?

anonymous · Answer

does that mean that there will be 2 points in common ; vertex below x-axis

anonymous · Answer

not necessarily.  you're right about the vertex being below the x axis, but also look at the coefficient of the x^2 term.  the negative means it's opening downward.  since the vertex is below the x axis, that means there are no points in common.