SOLUTION: Hello can you help me with this.
Calculate the value of the discriminant of x^2+4x+4=0
By examining the sign of the discriminant in part a, how many x-intercepts would the graph
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Question 120077: Hello can you help me with this.
Calculate the value of the discriminant of x^2+4x+4=0
By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+4x+4 have? Why?
Thanks
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The quadratic formula is:
The discriminant is
The equation given is of the form
The discriminant is 0, so the quadratic equation says there is 1 root
The curve touches the x-axis at 1 point (-2,0)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is the quadratic formula. The portion of the formula under the radical () is called the discriminant because it discriminates as to the type of roots for a given set of coefficients a, b, and c.
if , then the two roots of are real and unequal.
if , then the two roots of are real and equal.
if , then the two roots of are a complex conjugate pair.
In the problem given, , , and , so . This means that the two roots of are real and equal, therefore the graph of intersects the x axis at one point -- because both of the roots of the quadratic equation exist at the same point.
The following illustrates the graphs of (red graph, discriminant positive), (green graph, discriminant zero), and (blue graph, discriminant negative)
Hope this helps,
John
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