Question 704852: 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 = 2x2 + x + 3
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
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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 = 2x2 + x + 3
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
.
The discriminant determines the nature and number of roots.
Discriminant:
b^2 - 4ac
plugging in the coefficients:
1^2 - 4(2)(3)
1 - 24
-23
Since, it is NEGATIVE (no real roots) and the parabola opens upwards:
no points in common; vertex ABOVE x-axis
(BUT, you don't have this choice)
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