Question 66620: I'M HAVING A REALLY HARD TIME TRYING TO FIGURE THIS OUT. PLEASE HELP.
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. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation. In the real world, where might these imaginary numbers be used?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation. In the real world, where might these imaginary numbers be used?
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The discriminant determines if the roots of a quadratic equation are
Real and unequal if b^2-4ac> 0; for example if b=10, a=1,c=2;
In this case the graph will pass through the x-axis at two points.
Real but equal if b^2-4ac=0 : for example if b=6, a=9, c=4: in this
case the graph will touch but not pass through the x-axis.
or both Imaginary if b^2-4ac<0; for example if b=2, a=9, c=4: in this
case the graph stay above or entirely below the x axis.
Cheers,
Stan H.
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