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

Question

y=x^2+6x-4 type all x-intercepts. 

 

Type answers in correct from. 

Answer 1

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)