document.write( "Question 1041002: Q: For some constant α,the graph of a quadratic function f(x)= -x^2+2αx is a parabola with x intercept at A and B and vertex C.If the area of a triangle whose vertices are A B and C equals 125,what is the value of α? \n" ); document.write( "
Algebra.Com's Answer #655919 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
So you can look at the parabola, in terms of its roots.
\n" ); document.write( "\"y=-x%28x-2%2Aalpha%29\"
\n" ); document.write( "So the roots occur at \"x=0\" and \"x=2%2Aalpha\" to the base of the triangle which equals the distance between the roots is,
\n" ); document.write( "\"b=2%2Aalpha\"
\n" ); document.write( "So convert the parabola to vertex form,
\n" ); document.write( "\"y=-x%5E2%2B2%2Aalpha%2Ax\"
\n" ); document.write( "\"y=-%28x%5E2-2%2Aalpha%2Ax%2B%28alpha%29%5E2%29%2B%28alpha%29%5E2\"
\n" ); document.write( "\"y=-%28x-alpha%29%5E2%2B%28alpha%29%5E2\"
\n" ); document.write( "So the vertex is the maximum value of the parabola and the distance from the x-axis equals the height of the triangle governed by the term \"%28alpha%29%5E2\".
\n" ); document.write( "The area of the triangle is,
\n" ); document.write( "\"A=%281%2F2%29bh\"
\n" ); document.write( "\"A=%281%2F2%292%2Aalpha%2Aalpha%5E2\"
\n" ); document.write( "\"alpha%5E3=125\"
\n" ); document.write( "\"alpha=5\"
\n" ); document.write( " \n" ); document.write( "
\n" );