Search 75,676 tutors
FIND TUTORS
Ask a question
0 0

y=x^2+6x-4 type all x-intercepts

Tutors, please sign in to answer this question.

1 Answer

The firs thing you need to do in this type of problem is factor it.  First, I look at the leading coefficient of x^2.  As there is no coefficient given, you can leave it as x:
 
(x      )(x      )
 
I then look at the last number (in this case a -4)  The two factors of -4 are +/- 2 and 4 and 1.
 
(x-2)(x+2)   or  (x-4)(x+1)  or   (x-1)(x+4)
 
If I were to FOIL these though, I would find that I could not get a positive 6x. At this point I would use the quadratic formula:
 
x= - b +/- (√(b2-4ac)/2a
x = (-6 + √(62-4(1)(-4))/2(1)    and   x = -6 - √(62-4(1)(-4))/2(1)
x = -6 + √(36-(-16))/2            and   x = -6 - √(52)/2
x = -6 + √(52)/2                     and   x = -6 - √(52)/2
 
√(52) -> √13 * √4  -> 2√13
 
x = (-6 + 2√13)/2                   and   x = (-6 - 2√13)/2
x = -3 + √13                         and   x = -3 - √13             (Exact Answers)
x = .61                                  and    x = -6.6                 (Decimal Answers)