Question 143579This question is from textbook prentice hall algebra 1
: How do I solve? Use the dicriminant to determine whether the graph of each quadratic function intersects the x-axis in zero, one, or two points:
p=-3q^2+4q+2
This question is from textbook prentice hall algebra 1
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! calculate the discriminant __ b^2-4ac (it is the quantity under the square root in the quadratic formula)
if >0 then 2 points (roots)
if =0 then 1 point (double root)
if <0 then 0 points (no real roots)
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! The discriminant of a quadratic equation ( )is:  which is the radicand (the contents under the radical sign) of the quadratic formula.
If the discriminant is negative, the function will have two complex conjugate solutions (roots) and the graph of the function never intersects the x-axis.
If the discriminant is zero, the function will have one real solution (a double root) which is really two identical solutions which means that the graph of the function will just touch, but not cross, the x-axis.
If the discriminant is positive, the function will have two real solutions and the graph will cross the x-axis at two points.
Let's look at your equation:
 Here, a = -3, b = 4, and c = 2
The disciminant, D, is:
 It's positive so there are two real solutions (roots) and the graph crosses the x-axis at two points.
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