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f(x) = -0.1x^2 + 3.2x - 3.5 Find the x intercepts of the parabola. Thanks!
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High School Teacher
On a parabola, the x intercepts exist, of course, along the x-axis. this means that, at these points y=0. Therefore, solve the equation where y=0 and hence:
`-0.1x^2+3.2x - 3.5 = 0`
To make it easier to work with multiply by -1 and note the symbol changes :
`0.1x^2 - 3.2x +3.5 =0`
It may be easier to work with whole numbers rather than decimal fractions and, if preferred, multiply the equation by 10:
`x^2 - 32x +35 = 0`
Use the quadratic formula `(-b+- sqrt(b^2-4ac))/(2a)`
where a=1;b=-32; c=35
`x =(-(-32) +-sqrt((32^2)- 4(1)(35)))/(2(1))`
`therefore x= (32+-sqrt(1024-140))/2`
`therefore x= (32 +sqrt884)/2` OR `x=(32-sqrt884)/2`
`therefore x = 30.866` OR `x=1.134`
therefore the x-intercepts are (30.866;0) and (1.134; 0)
Posted by durbanville on April 29, 2013 at 10:01 PM (Answer #1)
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