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