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

Algebra ->  Human-and-algebraic-language -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+4x+%2B+4++=0
The quadratic formula is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
The discriminant is +b%5E2-4%2Aa%2Ac+
The equation given is of the form ax%5E2+%2B+bx+%2B+c+=+0
+b%5E2-4%2Aa%2Ac+=+4%5E2+-+4%2A1%2A4
4%5E2+-+4%2A1%2A4+=+0
The discriminant is 0, so the quadratic equation says there is 1 root
%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+=+-b%2F%282a%29
-b%2F%282a%29+=+-4%2F%282%2A1%29
The curve touches the x-axis at 1 point (-2,0)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+4x+%2B+4%29+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ is the quadratic formula. The portion of the formula under the radical (b%5E2-4ac) is called the discriminant because it discriminates as to the type of roots for a given set of coefficients a, b, and c.

if b%5E2-4ac%3E0, then the two roots of ax%5E2%2Bbx%2Bc=0 are real and unequal.

if b%5E2-4ac=0, then the two roots of ax%5E2%2Bbx%2Bc=0 are real and equal.

if b%5E2-4ac%3C0, then the two roots of ax%5E2%2Bbx%2Bc=0 are a complex conjugate pair.

In the problem given, a=1, b=4, and c=4, so b%5E2-4ac=4%5E2-4%281%29%284%29=16-16=0. This means that the two roots of x%5E2%2B4x%2B4=0 are real and equal, therefore the graph of f%28x%29=x%5E2%2B4x%2B4 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 f%28x%29=x%5E2%2B4x%2B3 (red graph, discriminant positive), f%28x%29=x%5E2%2B4x%2B4 (green graph, discriminant zero), and f%28x%29=x%5E2%2B4x%2B5 (blue graph, discriminant negative)

graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B4x%2B3%2Cx%5E2%2B4x%2B4%2Cx%5E2%2B4x%2B5%29

Hope this helps,
John