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

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hkj1385's profile pic

Posted on

To find the x-intercepts, 'y' must be equal to zero

i.e., -0.1*(x^2) + 3.2x - 3.5 = 0

Multiplying both sides by 10, we get

or, -(x^2) + 32x - 35 = 0

Multiplying both sides by -1, we get

or, (x^2) - 32x + 35 = 0

or, {(x^2) - 2*(1*16*x) + (16^2)} - 231 = 0

or, {(x-16)^2} - 231 = 0

or, {(x-16)^2} = 231

or, (x-16) = +sqrt(231)  or - sqrt(231)

or, x = [16 + sqrt(231)] or [16 - sqrt(231)]

Thus, the x-intercepts are [16 + sqrt(231)] or [16 - sqrt(231)]

jasminehems's profile pic

Posted on

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:


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


oldnick's profile pic

Posted on


we can rwrite y so:


so  `y=0 rArr` `x^2-32x+35=0`

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





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




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