SOLUTION: 5) a) Calculate the value of the discriminant of x^2+4x+4=0 b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+4x+4 have?

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 5) a) Calculate the value of the discriminant of x^2+4x+4=0 b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+4x+4 have?      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 90545: 5)
a) Calculate the value of the discriminant of x^2+4x+4=0
b) 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?
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
Discriminant:
D=b%5E2-4ac

D=4%5E2-4%281%29%284%29 Plug in a=1, b=4, a=4

D=16-4%281%29%284%29 Square 4 to get 16

D=16-16%29 Multiply -4%2A4%2A1 to get -16

D=0 Combine like terms


So a discriminant of zero means there is only one x-intercept

Remember, the quadratic formula is

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where the discriminant is D=b%5E2-4ac

So when you perform the quadratic formula, you would get

Plug the discriminant and the given values into the formula

Take the square root


So the expression breaks up to:

or

or Add/subtract 0

or Simplify

So we can see that the two values are the same answer. So this means we only get one x-intercept