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Math Help - standard form to intercept form

  1. #1
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    standard form to intercept form

    Hi; Just need to check some things out about conversion. convert 2/3x^2 - 12x + 50 to intercept form.How I did it. 2/3x^2 - 12x = - 50 2x^2 - 36x = - 150 x^2 - 18x = -75complete the square x^2 - 18x + 81 = -75 + 81 (x - 9)(x - 9) = 6 (x - 9)^2 = 6 (x - 9) = +,-sqrt6 x = 9 - sqrt6 x = 9 + sqrt6If these are the solutions to x why do I have an intercept form of 2/3(x - 11.4)(x - 6.6)ie why does p and q take the values of x?Thanks.
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  2. #2
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    Re: standard form to intercept form

    Because that is what "intercept" means- the points where the graph crosses or "intercepts" the x-axis. The fact the roots of (2/3)x^2- 12x+ 50= 0 at x= 9+ sqrt(6) and x= 9- sqrt(x) means that the graph "intercepts" the x-axis at (9+ sqrt(6), 0) and (9- sqrt(6), 0).

    (If I were you I would NOT approximate 9+ sqrt(6) by 11.4 and 9- sqrt(6) by 6.6. Surely, it is not that hard to use the actual values?)
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  3. #3
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    Re: standard form to intercept form

    Thank you.
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