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

1 point in common; vertex on x-axis
       2 points in common; vertex below x-axis
       2 points in common; vertex above x-axis
       no points in common; vertex below x-axis

anonymous · Answer

are you familiar with the formula to find the vertex

anonymous · Answer

Vertex Coordinates are gicen by the formula:
$$V(\frac{ -b }{ 2a },\frac{ -\Delta }{ 4a })$$
now a=-2;
       b=1;
        delta=25>0 it means the parabola has two points in common
Calculate the vertex coordinates with the formula and you have your answer