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 84020: 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.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This is an EXCELLENT question! When you solve the quadratic equation if the discriminant is POSITIVE, then there will be TWO distinct real roots. If is NEGATIVE, then there will be NO real roots. If is ZERO, then there will be only ONE real root, of multiplicity 2.
Now, if you graph the quadratic function , the ROOTS of the quadratic equation described in the previous paragraph correspond to the ZEROS (that is, the x-intercepts) of the graph of the quadratic function.
Likewise, the NUMBER of roots in the quadratic equation corresponds to the NUMBER of x-intercepts of the quadratic function.
If the discriminant of the quadratic function is POSITIVE, then there will be TWO x-intercepts. For example: , the discriminant is POSITIVE, since . There are TWO x-intercepts at x= 2 and at x= -2.
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If the discriminant of the quadratic function is NEGATIVE, then there will be NO x-intercepts. For example: , the discriminant is NEGATIVE, . Notice that there are NO x-intercepts, since the graph does not touch or cross the x-axis.
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If the discriminant is ZERO, then there will be only ONE x-intercept, and it will be of multiplicity 2. For example: , the discriminant is ZERO . There is ONE x-intercept at x= 0, and it has a multiplicity of 2.
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R^2 at SCC
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