Question 171709
In the equation ax^2 + bx + c=0,  the value of b^2 -4ac is called the determinant of the quadratic equation.
What does the value tell you about the real roots of the equation?
Ans: 
If b^2-4ac < 0 there are no Real Number roots.
If b^2-4ac = 0 there are two equal Real Number roots.
If b^2-4ac > 0 there are two unequal Real Number roots.
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Part 2, they don't want the graph.  Given the equation,determine how many x intercepts the parabola has. And whether its vertix lies above or below or on the axis.
If b^2-4ac < 0 there are no x-intercepts; vertex above or below and graph
does not intersect the x-axis.
If b^2-4ac = 0 the graph touches the x-axis at one point: vertex on x-axis
If b^2-4ac > 0 the graph intersects the x-axis at two points: vertex above or below and graph passes thru the x-axis.
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Cheers,
Stan H.