SOLUTION: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
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-> SOLUTION: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
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Question 51310: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.
You can put this solution on YOUR website! Notice the THREE parts to this solution:
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CASE I:
Discriminant is positive:
There are TWO real solutions. The implication for the graph of is that the graph crosses the x axis at TWO points.
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CASE II:
Discriminant is zero:
There is ONLY ONE real solution. The implication for the graph of is that the graph touches the x axis at only one point, but it does NOT cross the x axis.
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CASE III:
Discriminant is negative:
There are NO real solutions. The implication for the graph of is that the graph never touches nor crosses the x axis.
This is a VERY important concept, especially with graphing calculators!! Congratulations on an excellent question!!
