document.write( "Question 265636: The graph of a polynomial has x-intercepts at 1, -2, and 10 and passes through the point (2,-32). Determine the equation of the function in factored form. \n" ); document.write( "

Algebra.Com's Answer #195297 by roseo(33) $\"\"$ $\"About$

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Because 1,-2, and 10 are x-intercepts or zeros of the polynomial then (x-1), (x+2), and (x-10) are factors of the polynomial.
\n" ); document.write( "So we know that
\n" ); document.write( "y = a(x-1)(x+2)(x-10) is our polynomial and all we have to do is find a and the point (2,-32) gives us an x and y to put in the function to determine a.
\n" ); document.write( "-32 = a (2-1)(2+2)(2-10)
\n" ); document.write( "-32 = a (1)(4)(-8)
\n" ); document.write( "-32 = -32a
\n" ); document.write( "therefore a = 1
\n" ); document.write( "So the polynomial y = 1(x-1)(x+2)(x-10) will pass through (2,-32) \n" ); document.write( "

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