Homework Help

`y = -0.1x^2 + 3.2x - 3.5` find the x-intercepts by factoring.

user profile pic

loishy | Student, Grade 10 | Salutatorian

Posted April 26, 2013 at 7:22 PM via web

dislike 3 like

`y = -0.1x^2 + 3.2x - 3.5`

find the x-intercepts by factoring.

2 Answers | Add Yours

user profile pic

jasminehems | Student, Undergraduate | Honors

Posted April 27, 2013 at 2:30 AM (Answer #3)

dislike 2 like

Is this a trick question?  I tried every factoring I could find of 3.5 and .1, but none of them would give me 3.2 when I FOILed to check my answer.  I resorted to using the Quadratic Formula, and I found that the solutions are irrational numbers.  If the solutions are irrational, then this problem cannot be solved by factoring. 

I see. Can the x-intercepts be found any other way.

For any Quadratic, whether it is factorable or not, you can find the exact zeros by using the Quadratic Formula:

 `-b+-sqrt(b^2-4(a)(c))/(2(a))`

Where your `a` is your leading coefficient, or -0.1, your `b` is 3.2, and your `c` is -3.5. Just remember:

`y=ax^2+bx+c`

user profile pic

oldnick | Valedictorian

Posted April 27, 2013 at 3:17 AM (Answer #4)

dislike 0 like

`y=-0.1x^2+3.2x-3.5`

we can rwrite y so:

`y=-1/10(x^2-32x+35)`

so  `y=0 rArr` `x^2-32x+35=0`

`x^2-32x+256+35= 256`

`(x-16)^2=256-35`

`(x-16)^2=221`

`x-16=+-sqrt(221)`

`x=16+-sqrt(221)`  

are the solutions required:  `x_1=30.86606875`  `x_2=1.13393125` 

 

 

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes